×

zbMATH — the first resource for mathematics

Variety of integrable cases in dynamics of low- and multi-dimensional rigid bodies in nonconservative force fields. (English. Russian original) Zbl 1353.70019
J. Math. Sci., New York 204, No. 4, 379-530 (2015); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 125, 5-254 (2013).
Summary: This paper is a survey of integrable cases in dynamics of two-, three-, and four-dimensional rigid bodies under the action of a nonconservative force field. We review both new results and results obtained earlier. Problems examined are described by dynamical systems with so-called variable dissipation with zero mean.

MSC:
70E40 Integrable cases of motion in rigid body dynamics
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37N05 Dynamical systems in classical and celestial mechanics
70-02 Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
70E18 Motion of a rigid body in contact with a solid surface
70E45 Higher-dimensional generalizations in rigid body dynamics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] S. A. Agafonov, D. V. Georgievskii, and M. V. Shamolin, “Some actual problems of geometry and mechanics. Abstract of sessions of workshop ‘Actual Problems of Geometry and Mechanics’,” in: Contemporary Mathematics. Fundamental Directions [in Russian], 23 (2007), p. 34.
[2] S. A. Agafonov, D. V. Georgievskii, and M. V. Shamolin, “On woman’s role in the development of Contemporary Mechanics. Abstract of sessions of workshop ‘Actual Problems of Geometry and Mechanics’,” in: Contemporary Mathematics and Its Applications [in Russian], 76, Geometry and Mechanics (2012), p. 3.
[3] Aidagulov, RR; Shamolin, MV, A certain improvement of convey algorithm, Vestn. MGU, Ser. 1, Mat., Mekh., 3, 53-55, (2005)
[4] R. R. Aidagulov and M. V. Shamolin, “Archimedean uniform structure,” in: Contemporary Mathematics, Fundamental Directions [in Russian], 23, Moscow (2007), pp. 46-51.
[5] R. R. Aidagulov and M. V. Shamolin, “Varieties of continuous structures,” in: Contemporary Mathematics, Fundamental Directions [in Russian], 23, Moscow (2007), pp. 71-86. · Zbl 0107.07103
[6] R. R. Aidagulov and M. V. Shamolin, “General spectral approach to continuous medium dynamics,” in: Contemporary Mathematics, Fundamental Directions [in Russian], 23, Moscow (2007), pp. 52-70.
[7] Aidagulov, RR; Shamolin, MV, Phenomenological approach to definition of interphase forces, Dokl. Ross. Akad. Nauk, 412, 44-47, (2007)
[8] R. R. Aidagulov and M. V. Shamolin, “Groups of colors,” in: Contemporary Mathematics and Its Applications [in Russian], 62, Geometry and Mechanics (2009), pp. 15-27. · Zbl 1214.16029
[9] R. R. Aidagulov and M. V. Shamolin, “Averaging operators and real equations of hydromechanics,” in: Contemporary Mathematics and Its Applications [in Russian], 65, Mathematical Physics, Combinatorics, and Optimal Control (2009), pp. 31-47. · Zbl 1288.76004
[10] R. R. Aidagulov and M. V. Shamolin, “Pseudodifferential operators in the theory of multiphase, multi-rate flows,” in: Contemporary Mathematics and Its Applications [in Russian], 65, Mathematical Physics, Combinatorics, and Optimal Control (2009), pp. 11-30. · Zbl 1288.35493
[11] Aidagulov, RR; Shamolin, MV, Integration formulas of tenth order and higher, Vestn. MGU, Ser. 1, Mat., Mekh., 4, 3-7, (2010)
[12] H. Airy, The Soaring of Birds, “Nature”, vol. XXVIII, 1.596.
[13] Al’ev, GA, Spatial problem of submergence of a disk into an incompressible fluid, Izv. Akad. Nauk SSSR, Mekh. Zh. Gaz., 1, 17-20, (1988)
[14] V. V. Amel’kin, N. A. Lukashevich, and A. P. Sadovskii, Nonlinear Oscillations in Second-Order Systems [in Russian], BGU, Minsk (1982).
[15] A. A. Andronov, Collection of Works [in Russian], Izd. Akad Nauk SSSR, Moscow (1956).
[16] A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier, Qualitative Theory of Second-Order Dynamical Systems [in Russian], Nauka, Moscow (1966). · Zbl 0282.34022
[17] A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier, Bifurcation Theory of Dynamical Systems on the Plane [in Russian], Nauka, Moscow (1967).
[18] Andronov, AA; Pontryagin, LS, Rough systems, Dokl. Akad. Nauk SSSR, 14, 247-250, (1937)
[19] D. V. Anosov, “Geodesic flows on closed Riemannian manifolds of negative curvature,” Trudy Mat. Inst. Akad. Nauk SSSR, 90 (1967). · Zbl 0176.19101
[20] P. Appel, Theoretical Mechanics, Vols. I, II [Russian translation], Fizmatgiz, Moscow (1960).
[21] S. Kh. Aranson, “Dynamical systems on two-dimensional manifolds,” in: Proceedings of the 5th International Conference in Nonlinear Oscillations, Vol. 2 [in Russian], Institute of Mathematics, Academy of Sciences of UkrSSR (1970). · Zbl 0286.34074
[22] S. Kh. Aranson and V. Z. Grines, “Topological classification of flows on two-dimensional manifolds,” Usp. Mat. Nauk,41, No. 1 (1986). · Zbl 0615.58015
[23] Arnol’d, VI, Hamiltonian property of Euler equations of rigid body dynamics in ideal fluid, Usp. Mat. Nauk, 24, 225-226, (1969) · Zbl 0181.54204
[24] V. I. Arnol’d, V. V. Kozlov, and A. I. Neishtadt, “Mathematical aspects of classical and celestial mechanics,” in: Progress in Science and Technology, Series on Contemporary Problems in Mathematics, Fundamental Direction [in Russian], 3, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (1985). · Zbl 0885.70001
[25] D. Arrowsmith and C. Place, Ordinary Differential Equations. Qualitative Theory with Applications [Russian translation], Mir, Moscow (1986). · Zbl 0671.34001
[26] E. A. Barbashin and V. A. Tabueva, Dynamical Systems With Cylindrical Phase Space [in Russian], Nauka, Moscow (1969). · Zbl 0212.43404
[27] N. N. Bautin and E. A. Leontovich, Methods and Tools for Qualitative Study of Dynamical Systems on the Plane [in Russian], Nauka, Moscow (1976). · Zbl 0785.34004
[28] V. V. Beletskii and A. M. Yanshin, Influence of Aerodynamical Forces on Rotational motion of Artificial Satellites [in Russian], Naukova Dumka, Kiev (1984).
[29] Belyaev, AV, On many-dimensional body motion with clumped point in gravity force field, Mat. Sb., 114, 465-470, (1981)
[30] I. Bendixon, “On curves defined by differential equations,” Usp. Mat. Nauk, 9 (1941). · Zbl 0815.34002
[31] G. D. Birkhoff, Dynamical Systems [ Russian translation], Gostekhizdat, Moscow-Leningrad (1941).
[32] Yu. K. Bivin, “Change of direction of motion of a rigid body on separation boundary of a medium,” Izv. Akad. Nauk SSSR, Mekhanika Tverdogo Tela, No. 4, 105-109 (1981).
[33] Yu. K. Bivin, V. V. Viktorov, and L. L. Stepanov, “Study of rigid body motion in a clayey medium,” Izv. Akad. Nauk SSSR, Mekhanika Tverdogo Tela, No. 2, 159-165 (1978).
[34] Yu. K. Bivin, Yu. M. Glukhov, and Yu. V. Permyakov, “Vertical entrance of rigid bodies into water,” Izv. Akad. Nauk SSSR, Mekhanika Zhidkosti Gaza, No. 6, 3-9 (1985).
[35] M. Blix, Une Nouvelle Theorie sur le Vol a Viole des Oiseaux, “Revue generale sciences pures et appliquees” (1890).
[36] O. I. Bogoyavlenskii, Methods of Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics [in Russian], Nauka, Moscow (1980).
[37] Bogoyavlenskii, OI, Dynamics of a rigid body with \(n\) ellipsoidal holes filled with a magnetic fluid, Dokl. Akad. Nauk SSSR, 272, 1364-1367, (1983)
[38] Bogoyavlenskii, OI, Some integrable cases of Euler equation, Dokl. Akad. Nauk SSSR, 287, 1105-1108, (1986)
[39] Bogoyavlenskii, OI; Ivakh, GF, Topological analysis of integrable cases of V. A. Steklov, Usp. Mat. Nauk, 40, 145-146, (1985)
[40] Borisenok, IT; Lokshin, BY; Privalov, VA, On flight dynamics of axially-symmetric rotating bodies in air, Izv. Akad Nauk SSSR, Mekhanika Tverdogo Tela, 2, 35-42, (1984)
[41] Borisenok, IT; Shamolin, MV, Solution of differential diagnosis problem, Fund. Prikl. Mat., 5, 775-790, (1999) · Zbl 0967.93033
[42] I. T. Borisenok and M. V. Shamolin, “Solution of differential diagnosis problem by statistical trial method,” Vestn. MGU, Ser. 1, Mat., Mekh., No. 1, 29-31 (2001).
[43] N. Bourbaki, Integration [Russian translation], Nauka, Moscow (1970). · Zbl 0213.07501
[44] N. Bourbaki, Lie Groups and Algebras [Russian translation], Mir. Moscow (1972). · Zbl 0249.22001
[45] Brailov, AV, Some cases of complete integrability of Euler equations and applications, Dokl. Akad. Nauk SSSR, 268, 1043-1046, (1983)
[46] A. D. Bryuno, Local Method of Nonlinear Analysis of Differential Equations [in Russian], Nauka, Moscow (1979). · Zbl 0496.34002
[47] Burov, VA, Non-integrability of equations of satellite plane oscillations on an elliptic orbit, Vestn. MGU, Ser. 1, Mat. Mekh., 1, 71-73, (1984) · Zbl 0598.70033
[48] G. S. Byushgens and R. V. Studnev, Dynamics of Longitudinal and Lateral Motion [in Russian], Mashinostroenie, Moscow (1969).
[49] G. S. Byushgens and R. V. Studnev, Airplane Dynamics. Spatial Motion [in Russian], Mashinostroenie, Moscow (1988).
[50] S. A. Chaplygin, “On motion of heavy bodies in an incompressible fluid,” in: A Complete Collection of Works [in Russian], Vol. 1, Izd. Akad. Nauk SSSR, Leningrad (1933), pp. 133-135.
[51] S. A. Chaplygin, Selected Works [in Russian], Nauka, Moscow (1976).
[52] Dubrovin, BA; Novikov, SP, On Poisson brackets of hydrodynamical type, Dokl. Akad. Nauk SSSR, 279, 294-297, (1984)
[53] B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry. Theory and Applications [in Russian], Nauka, Moscow (1979).
[54] V. A. Eroshin, “Plate reflection from ideal incompressible fluid surface,” Vestn. MGU, Ser. 1., Mat., Mekh., No. 6, 99-104 (1970).
[55] Eroshin, VA, Submergence of a disk into a compressible fluid at an angle to a free surface, Izv. Akad. Nauk SSSR, Mekhanika Zhidkosti Gaza, 2, 142-144, (1983)
[56] V. A. Eroshin, “Experimental study of compression forces excited in an elasic cylinder under its entrance into water,” in: Applied Problems of Solidity and Plasticity, Issue 46 [in Russian], Gor’kii State University, Gor’kii (1990), pp. 54-59.
[57] V. A. Eroshin, “Penetration of an elastic cylinder into high-speed water,” Preprint, No. 5, Insitute of Mechanics, Moscow State University, Moscow (1991).
[58] Eroshin, VA, Experimental study of entrance of an elastic cylinder into high-speed water, Izv. Ross. Akad. Nauk, Mekhanika Zhidkosti Gaza, 5, 20-30, (1992)
[59] V. A. Eroshin, G. A. Konstantinov, N. I. Romanenkov and Yu. L. Yakimov, “Experimental finding of pressure on a disk under its submergence into a compressible fluid at an angle to a free surface,” Izv. Akad. Nauk SSSR, Mekhanika Zhidkosti Gaza, No. 2, 21-25 (1988).
[60] Eroshin, VA; Konstantinov, GA; Romanenkov, NI; Yakimov, YL, Experimental finding of hydrodynamical force moment under an asymmetric penetration of a disk into a compressible fluid, Izv. Ross. Akad. Nauk, Mekhanika Zhidkosti Gaza, 5, 88-94, (1990)
[61] V. A. Eroshin, A. V. Plyusnin, Yu. A. Sozonenko, and Yu. L. Yakimov, “On methodology for stadying bend oscillations of an elastic cylinder under its entrance into water at an angle to a free surface,” Izv. Akad. Nauk SSR, Mekhanika Zhidkosti Gaza, No. 6, 164-167 (1989).
[62] V. A. Eroshin, V. A. Privalov, and V. A. Samsonov, “Two model problems of body motion in a resisting medium,” in: Collection of Scientific-Methodological Papers in Theoretical Mechanics [in Russian], Issue 18, Nauka, Moscow (1987), pp. 75-78.
[63] Eroshin, VA; Romanenkov, NI; Serebryakov, IV; Yakimov, YL, Hydrodynamical forces under a shock of blunt bodies on compressible fluid surface, Izv. Ross. Akad. Nauk, Mekhanika Zhidkosti Gaza, 6, 44-51, (1980)
[64] V. A. Eroshin, V. A. Samsonov, and M. V. Shamolin, “On motion of a body under streamline flow,” in: Abstracts of All-Union Conference on Stability of Motion, Oscillations of Mechanical Systems, and Aerodynamics, Moscow, February 2-4, 1988 [in Russian], Moscow Aviation Institute, Moscow (1988), p. 21.
[65] V. A. Eroshin, V. A. Samsonov, and M. V. Shamolin, “Mathematical modelling in problem of body drag in a medium under streamline flow,” in: Abstracts of Chebyshev Readings, Vestn. MGU, Ser. 1, Mat., Mekh.,6, 17 (1995).
[66] Eroshin, VA; Samsonov, VA; Shamolin, MV, Model problem of body drag in a resisting medium under streamline flow, Izv. Ross. Akad. Nauk, Mekhanika Zhidkosti Gaza, 3, 23-27, (1995)
[67] R. R. Fakhrudinova and M. V. Shamolin, “On preservation of phase volume in ‘zero mean’ variable dissipation systems,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics’ [in Russian], Fund. Prikl. Mat., 7, No. 1, 311 (2001).
[68] R. R. Fakhrudinova and M. V. Shamolin, “On preservation of phase volume in ‘zero mean’ variable dissipation systems,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Contemporary Mathematics, Fundamental Directions [in Russian], 23 (2007), p. 22.
[69] Fomenko, AT, Realizations of cycles in compact symmetric spaces by totally geodesic submanifolds, Dokl. Akad. Nauk SSSR, 195, 789-792, (1970)
[70] D. V. Georievskii, V. V. Trofimov, and M. V. Shamolin, “Geometry and mechanics: problems, approaches, and methods,” in: Abstracts of sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Fund. Prikl. Mat., 7, No. 1, 301 (2001).
[71] D. V. Georgievskii, V. V. Trofimov, and M. V. Shamolin, “Geometry and mechanics: problems, approches, and methods,” in: Abstract of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Contemporary Mathematics, Fundamental directions [in Russian] 23 (2007), p. 16.
[72] D. V. Georgievskii, V. V. Trofimov, and M. V. Shamolin, “On certain topological invariants of flows with complex potential,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Fund. Prikl. Mat., 7, No. 1, 305 (2001).
[73] D. V. Georgievskii, V. V. Trofimov, and M. V. Shamolin, “On certain topological invariants of flows with complex potential,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Contemporary Mathematics, Fundamental Directions [in Russian], 23 (2007), p. 19.
[74] Georgievskii, DV; Shamolin, MV, Kinematics and mass geometry of a rigid body with fixed point in ℝ\^{}{\(n\)}, Dokl. Ross. Akad. Nauk, 380, 47-50, (2001)
[75] D. V. Georgievskii and M. V. Shamolin, “On kinematics of a rigid body with fixed point in ℝ\^{}{\(n\)},” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Fund. Prikl. Mat.,7, No. 1, 315 (2001).
[76] Georgievskii, DV; Shamolin, MV, Generalized dynamical Euler equations for a rigid body with fixed poit in ℝ\^{}{\(n\)}, Dokl. Ross. Akad. Nauk, 383, 635-637, (2002)
[77] Georgievskii, DV; Shamolin, MV, First integrals of motion of equations of motion for a generalized gyroscope in ℝ\^{}{\(n\)}, Vestn. MGU, Ser. 1, Mat., Mekh., 5, 37-41, (2003) · Zbl 1127.70003
[78] D. V. Georgievskii and M. V. Shamolin, “Valerii Vladimirovich Trofimov,” in: Contemporary Mathematics, Fundamental Directions [in Russian] 23 (2007), pp. 5-6. · Zbl 1153.01325
[79] D. V. Georgievskii and M. V. Shamolin, “On kinematics of a rigid body with a fixed point in ℝ\^{}{\(n\)},” in: Abstracts of Session of Workshop ‘Actual Problems of Geometry and Mechanics,’ Contemporary Mathematics, Fundamental Directions [in Russian], 23 (2007), pp. 24-25.
[80] D. V. Georgievskii and M. V. Shamolin, “Generalized dynamical Euler equations for a rigid body with a fixed point in ℝ\^{}{\(n\)},” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Comtemporary Mathematics, Fundamental Directions [in Russian], 23 (2007), p. 30.
[81] D. V. Georgievskii and M. V. Shamolin, “First integrals for equations of motion of a generalized gyroscope in \(n\)-dimensional space,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics, Contemporary Mathematics, Fundamental Directions [in Russian], 23 (2007), p. 31.
[82] D. V. Georgievskii and M. V. Shamolin, “Sessions of the workshop of the Mathematics and Mechanics Department of Lomonosov Moscow State University, ‘Topical problems of geometry and mechanics’ named after V. V. Trofimov,” in: Contemporary Mathematics and Its Applications [in Russian], 65, Mathematical Physics, Combinatorics, and Optimal Control (2009), pp. 3-10. · Zbl 1180.00019
[83] D. V. Georgievskii and M. V. Shamolin, “Π-theorem of Dimensionality Theory. Abstract of sessions of workshop ‘Actual Problems of Geometry and Mechanics’,” in: Contemporary Mathematics and Its Applications [in Russian], 65, Mathematical Physics, Combinatorics, and Optimal Control (2009), p. 3. · Zbl 1180.00019
[84] D. V. Georgievskii and M. V. Shamolin, “Sessions of the workshop of the Mathematics and Mechanics Department of Lomonosov Moscow State University, ‘Topical problems of geometry and mechanics’ named after V. V. Trofimov,” in: Contemporary Mathematics and Its Applications [in Russian], 76, Geometry and Mechanics (2012), pp. 3-10. · Zbl 1260.00024
[85] D. V. Georgievskii and M. V. Shamolin, “Levi-Civita symbols, generalized vector products, and new integrable cases in mechanics of multidimensional bodies,” in: Contemporary Mathematics and Its Applications [in Russian], 76, Geometry and Mechanics (2012), pp. 22-39. · Zbl 1278.70007
[86] D. V. Georgievskii and M. V. Shamolin, “Levi-Civita symbols, generalized vector products, and new integrable cases in mechanics of multidimensional bodies. Abstract of sessions of workshop ‘Actual Problems of Geometry and Mechanics’,” in: Contemporary Mathematics and Its Applications [in Russian], 76, Geometry and Mechanics (2012), p. 9. · Zbl 1278.70007
[87] Georgievskii, DV; Shamolin, MV, Sessions of the workshop of the mathematics and mechanics department of lomonosov Moscow state university, ‘urgent problems of geometry and mechanics’ named after V. V. trofimov, J. Math. Sci., 154, 462-495, (2008) · Zbl 1299.01007
[88] Georgievskii, DV; Shamolin, MV, Sessions of the workshop of the mathematics and mechanics department of lomonosov Moscow state university, ‘urgent problems of geometry and mechanics’ named after V. V. trofimov, J. Math. Sci., 161, 603-614, (2009) · Zbl 1180.00019
[89] C. Godbillon, Differential Geometry and Analytical Mechanics [Russian translation], Mir, Moscow (1973).
[90] V. V. Golubev, Lectures on Analytical Theory of Differential Equations [in Russian], Gostekhizdat, Moscow-Leningrad (1950). · Zbl 0038.24201
[91] V. V. Golubev, Lectures on Integrating Equations of Heavy Body Motion Around a Fixed Point, Gostekhizdat, Moscow-Leningrad (1953). · Zbl 0051.15103
[92] Goryachev, DN, New cases of integrability of dynamical Euler equations, Warshaw. Univ. Izv., 3, 1-15, (1916)
[93] I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series Sums, and Derivatives [in Russian], Gostekhizdat, Moscow (1963).
[94] Ph. Griifits, Exterior Differential Systems and the Calculus of Variations [Russian translation], Mir, Moscow (1986).
[95] Grobman, DM, On homeomorphism of systems of differential equations, Dokl. Akad. Nauk SSSR, 128, 880-881, (1959) · Zbl 0100.29804
[96] Grobman, DM, Topological classification of neighborhoods of a singular point in \(n\)-dimensional space, Mat. Sb., 56, 77-94, (1962)
[97] D. A. Gudkov, “On concept of non-roughness and degrees of non-roughness for plane algebraic curves,” Mat. Sb.,67, No. 4 (1965).
[98] M. I. Gurevich, Jet Theory of Ideal Fluid [in Russian], Nauka, Moscow (1979).
[99] Ph. Hartman, Ordinary Differential Equations [Russian translation], Mir, Moscow (1970).
[100] Ivanova, TA, On Euler equations in models of theoretical physics, Mat. Zametki, 52, 43-51, (1992)
[101] A. Yu. Ishlinskii, Orientation, Gyroscopes, and Inertial Navigation [in Russian], Nauka, Moscow (1976).
[102] C. Jacobi, Lectures on Dynamics [Russian translation], ONTI, Moscow-Leningrad (1936).
[103] V. V. Kozlov, Qualitative Analysis Methods in Rigid Body Dynamics [In Russian], MGU, Moscow (1980). · Zbl 0557.70009
[104] Kozlov, VV, Hydrodynamics of Hamiltonian systems, Vestn. MGU, Ser. 1, Mat., Mekh., 6, 10-22, (1983) · Zbl 0552.76006
[105] Kozlov, VV, Integrability and non-integrability in Hamiltonian mechanics, Usp. Mat. Nauk, 38, 3-67, (1983)
[106] Kozlov, VV, The problem of rigid body rotation in a magnetic field, Izv. Akad. Nauk SSSR, Mekhanika Tverdogo Tela, 6, 28-33, (1985)
[107] Kozlov, VV, On rigid body fall in ideal fluid, Izv. Akad. Nauk SSSR, Mekhanika Tverdogo Tela, 5, 10-17, (1989)
[108] Kozlov, VV, The problem of heavy rigid body fall in a resisting medium, Vestn. MGU, Ser. 1, Mat., Mekh., 1, 79-87, (1990)
[109] Kozlov, VV; Kolesnikov, NN, On integrability of Hamiltonian systems, Vestn. MGU, Ser. 1, Mat., Mekh., 6, 88-91, (1979) · Zbl 0422.70022
[110] Kozlov, VV; Onishchenko, DA, Non-integrability of Kirchhoff equations, Dokl. Akad. Nauk SSSR, 266, 1298-1300, (1982)
[111] P. F. Komarov and M. V. Shamolin, “Optimization of accommodation of several cosmic devices at the rocket-vehicle”, in: Proc. Sixth Aero-Cosmic Congress (IAC’09), Moscow, August 23-27, 2009 [in Russian], Moscow (2009), pp. 132-135.
[112] G. Lamb, Hydrodynamics [Russian translation], Fizmatgiz, Moscow (1947).
[113] J. Leech, Classical Mechanics [Russian translation], IL, Moscow (1961).
[114] O. Liliental, Der Vogelflug als Grundlage der Fliegekunst, Berlin (1889).
[115] Lokshin, BY, On a certain motion of a rapidly rotating body in air, Vestn. MGU, Ser. 1, Mat., Mekh., 6, 93-98, (1970)
[116] Lokshin, BY, On stability of plane motion of a rapidly rotating symmetric body in atmosphere, Vestn. MGU, Ser. 1, Mat., Mekh., 6, 113-118, (1971) · Zbl 0261.70007
[117] Lokshin, BY, On screw motion of a rapidly rotating symmetric rigid body in air, Vestn. MGU, Ser. 1, Mat., Mekh., 4, 79-86, (1973)
[118] B. Ya. Lokshin, “On stability of stationary motoions of a rapidly rotating symetric rigid body in air,” Izv. Akad. Nauk SSSR, Mekhanika Tverdogo Tela, No. 2, 18-24 (1976).
[119] B. Ya. Lokshin, Yu. M. Okunev, V. A. Samsonov, and M. V. Shamolin, “Some integrable cases of rigid body spatial oscillations in a resisting medium,” in: Abstracts of Reports of XXI Scientific Readings in Cosmonautics, Moscow, January 28-31, 1997 [in Russian], Institute of History of Natural Sciences and Technics, Russian Academy of Sciences, Moscow (1997), pp. 82-83.
[120] B. Ya. Lokshin, V. A. Privalov, and V. A. Samsonov, An Introduction to Problem of Motion of a Body in a Resisting Medium [in Russian], MGU, Moscow (1986).
[121] B. Ya. Lokshin, V. A. Privalov, and V. A. Samsonov, An Introduction to Problem of Motion of a Point and a Body in a Resisting Medium [in Russian], MGU, Moscow (1992).
[122] A. M. Lyapunov, “A new case of integrability of equations of motion of a rigid body motion in a fluid,” in: A Collection of Works [in Russian], Vol. I, Izd. Akad. Nauk SSSR, Moscow (1954), pp. 320-324.
[123] Yu. I. Manin, “Algebraic aspects of theory of nonlinear differential equations,” in: Progress in Science and Technology, Series on Contemporary Problems in Mathematics [in Russian], 11, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (1978), pp. 5-112. · Zbl 0100.29804
[124] E.-J. Marey, Le Vol des Oiseaux, Chap. XX, Paris (1890).
[125] J. Marsden and M. McCracken,The Hopf Bifurcation and Its Applications [Russian translation], Mir, Moscow (1986).
[126] W. Miller, Symmetry and Separation of Variables [Russian translation], Mir, Moscow (1981).
[127] Yu. A. Mitropol’skii and O. B. Lykova, Integral Manifolds in Nonlinear Mechanics [in Russian], Nauka, Moscow (1973).
[128] A. V. Mokeev and M. V. Shamolin, “Some problems of differential diagnostics”, in: All-Russian Conference in Honour of 110th Anniversary of Mathematics Faculty of MPSU ‘Mathematics, Informatics and Methodology of Its Teaching. Moscow, March 14-16’ [in Russian], Moscow, MPSU (2011), pp. 72-74.
[129] L.-P. Mouillard, L’empire de l’Air, Paris (1881).
[130] Neimark, YI, On motions close to a double-asymptotic motion, Dokl. Akad. Nauk SSSR, 172, 1021-1024, (1967)
[131] V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations [in Russian], Gostekhizdat, Moscow-Leningrad (1949).
[132] Z. Nitetski, Introduction to Differential Dynamics [Russian translation], Mir, Moscow (1975).
[133] Novikov, SP; Schmeltzer, I, “periodic solutions of Kirchhoff equations for the free motion of a rigid body and an ideal fluid and extended lyusternik-shnirel’man-Morse theory, Funct. Anal. Pril., 15, 54-66, (1981)
[134] V. A. Odareev, Decompositional Analysis of Dynamics and Stability of Longitudinal Perturbed Motion of a Screencraft [in Russian], Doctor Dissertation, MGAI, Moscow (1995).
[135] Yu.M. Okunev and V. A. Sadovnichii, “Model dynamical systems of a certain problem of external ballistics and their analytical solutions,” in: Problems of Modern Mechanics [in Russian], MGU, Moscow (1998), pp. 28-46.
[136] Okunev, YM; Sadovnichii, VA; Samsonov, VA; Chernyi, GG, A complex for modelling flight dynamics problems, Vestn. MGU, Ser. 1, Mat., Mekh., 6, 66-75, (1996)
[137] Yu. M. Okunev and M. V. Shamolin, “On integrability in elementary functions of certain classes of complex nonautonomous equations,” in: Contemporary Mathematics and Its Applications [in Russian], 65, Mathematical Physics, Combinatorics and Optimal Control (2009), pp. 122-131.
[138] B. Onniere, Etude sur le vol plane, “L’Aeronaute” (1891).
[139] J. Palais and S. Smale, “Structural stability theorems,” in: A Collection of Translations. Mathematics [Russian translation], 13, No. 2, 145-155 (1969).
[140] J. Palis and W. De Melu, Geometric Theory of Dynamical Systems, An Introduction [Russian translation], Mir, Moscow (1986).
[141] A. von Parseval, Die Mechanik des Vogelflugs, Wisbaden (1889).
[142] S. E. Peal, Soaring of Birds, “Nature”, vol. XXVIII, 1.11. · Zbl 1180.00019
[143] Peixoto, M, On structural stability, Ann. Math., 2, 199-222, (1959) · Zbl 0084.08403
[144] Peixoto, M, Structural stability on two-dimensional manifolds, Topology, 1, 101-120, (1962) · Zbl 0107.07103
[145] Peixoto, M, On an approximation theorem of kupka and Smale, J. Diff. Eq., 3, 214-227, (1966) · Zbl 0153.40901
[146] Perelomov, AM, Several remarks on integration of equations of rigid body motion in ideal fluid, Funkts. Anal. Pril., 15, 83-85, (1981)
[147] V. A. Pliss, Nonlocal Problems of Oscillation Theory [in Russian], Nauka, Moscow-Leningrad (1964).
[148] V. A. Pliss, Integral Sets of Periodic Systems of Differential equations [in Russian], Nauka, Moscow (1967).
[149] N. V. Pokhodnya and M. V. Shamolin, “Some applications of fractal theory in dynamics,” in: All-Russian Conference in Honour of 110th Anniversary of Mathematics Faculty of MPSU ‘Mathematics, Informatics and Methodology of Its Teaching. Moscow, March 14-16, 2011’ [in Russian], Moscow, MPSU (2011), pp. 81-82.
[150] L. Prandtl and A. Betz, Ergebnisse der Aerodynamischen Versuchsanstalt zu G¨ottingen, Berlin (1932), 148 p. · JFM 53.0809.03
[151] Privalov, VA; Samsonov, VA, On stability of motion of a body auto-rotating in a flowing medium, Izv. Akad. Nauk SSSR, Mekhanika Tverdogo Tela, 2, 32-38, (1990)
[152] H. Poincaré, On Curves Defined by Differential Equations [Russian translation], OGIZ, Moscow-Leningrad (1947).
[153] H. Poincaré, New Methods in Celestial Mechanics, in: Selected Works [Russian translation], Vols. 1, 2, Nauka, Moscow (1971-1972).
[154] H. Poincaré, On Science [Russian translation], Nauka, Moscow (1983).
[155] Lord Rayleigh (J. W. Strutt), The Soaring of Birds, “Nature,” vol. XXVIII, 1.534. · Zbl 0598.70033
[156] R. Reissing, G. Sansone, and R. Conti, Qualitative Theory of Ordinary Differential Equations [Russian translation], Nauka, Moscow (1974).
[157] V. E. Ryzhova and M. V. Shamolin, “On some analogies in the problem of the motion of a body in a resisting medium,” in: Seventh Congress in Theoretical and Applied Mechanics, Moscow, August 15-21, 1991 [in Russian], Moscow (1991). · Zbl 1274.74112
[158] Sadetov, ST, Integrability conditions of Kirchhoff equations, Vestn. MGU, Ser. 1, Mat., Mekh., 3, 56-62, (1990)
[159] Sal’nikova, TV, On integrability of Kirchhoff equations in symmetric case, Vestn. MGU, Ser. 1, Mat., Mekh., 4, 68-71, (1985)
[160] Samsonov, VA, On quasi-stationary motions of mechanical systems, Izv. Akad. Nauk SSSR, Mekhanika Tverdogo Tela, 1, 32-50, (1978)
[161] V. A. Samsonov, Issues on Mechanics. Some Problems, Phenomena, and Paradoxes [in Russian], Nauka, Moscow (1980).
[162] V. A. Samsonov, V. A. Eroshin, G. A. Konstantinov, and V. M. Makarshin, “Two model problems on the motion of a body in a medium under streamline flow,” in: Scientific Report of Institute of Mechanics, Moscow State University [in Russian], No. 3427, Institute of Mechanics, Moscow State University, Moscow (1987).
[163] V. A. Samsonov, B. Ya. Lokshin, and V. A. Privalov, “Qualitative analysis,” in: Scientific Report of Institute of Mechanics, Moscow State University [in Russian], No. 3245, Institute of Mechanics, Moscow State University (1985). · Zbl 0800.70042
[164] Samsonov, VA; Shamolin, MV, Problem of the motion of a body in a resisting medium, Vestn. MGU, Ser. 1, Mat., Mekh., 3, 51-54, (1989)
[165] V. A. Samsonov and M. V. Shamolin, “On the motion of a body in a resisting medium,” in: Contemporary Problems of Mechanics and Technologies of Machine Industry, All-Union Conference, April, 16-18, 1989. Abstracts of Reports [in Russian], All-Union Institute for Scientific and Technical Information, Moscow (1989), pp. 128-129.
[166] V. A. Samsonov and M. V. Shamolin, “A model problem of the motion of a body in a medium with streamline flow,” Scientific Report of Institute of Mechanics, Moscow State University [in Russian], No. 3969, Institute of Mechanics, Moscow State University, Moscow (1990). · Zbl 0967.93033
[167] V. A. Samsonov and M. V. Shamolin, “A model problem of the motion of a body in a medium with streamline flow,” in: Nonlinear Oscillations of Mechanical Systems, Abstract of Reports of II All-Union Conference, September, 1990 [in Russian], Pt. 2, Gor’kii (1990), pp. 95-96.
[168] V. A. Samsonov and M. V. Shamolin, “Problem of body drag in a medium under streamline flow,” in: Scientific Report of Institute of Mechanics, Moscow State University [in Russian], No. 4141, Institute of Mechanics, Moscow State University, Moscow (1991).
[169] V. A. Samsonov, M. V. Shamolin, V. A. Eroshin, and V. M. Makarshin, “Mathematical modelling in problem of body drag in a resisting medium under streamline flow,” in: Scientific Report of Institute of Mechanics, Moscow State University [in Russian], No. 4396, Moscow (1995).
[170] G. Sansone, Ordinary Differential Equations. [Russian translation], IL, Moscow (1954).
[171] L. I. Sedov, Mechanics of a Continuous Medium [in Russian], Vols. 1, 2, Nauka, Moscow (1983-1984).
[172] H. Seifert and W. Threifall, Topology [Russian translation], Gostekhizdat, Moscow-Leningrad (1938).
[173] N. Yu. Selivanova and M. V. Shamolin, “Studying the interphase zone in a certain singularlimit problem,” in: Materials of Voronezh All-Russian Conference ‘Pontryagin Readings-XXII,’ Voronezh, May 3-9, 2011 [in Russian], Voronezh State University, Voronezh (2011), pp. 164-165.
[174] N. Yu. Selivanova and M. V. Shamolin, “Local solvability of a certain problem with free boundary,” Vestnik SamGU. Natural Sciences, No. 8(89), 86-94 (2011).
[175] N. Yu. Selivanova and M. V. Shamolin, “Local solvability of a one-phase problem with free boundary,” in: Materials of Voronezh Winter Mathematical School ‘Contemporary Methods of Function Theory and Related Problems,’ Voronezh, January 26-February 1, 2011 [in Russian], Voronezh State University, Voronezh (2011), p. 307.
[176] N. Yu. Selivanova and M. V. Shamolin, “Studying the interphase zone in a certain singularlimit problem,” in: Contemporary Mathematics and Its Applications [in Russian], 78, Partial Differential Equations and Optimal Control (2012), pp. 109-118.
[177] N. Yu. Selivanova and M. V. Shamolin, “Quasi-stationary Stefan problem with values at the front depending on its geometry,” in: Contemporary Mathematics and Its Applications [in Russian], 78, Partial Differential Equations and Optimal Control (2012), pp. 126-134.
[178] N. Yu. Selivanova and M. V. Shamolin, “Local solvability of the capillary problem,” in: Contemporary Mathematics and Its Applications [in Russian], 78, Partial Differential Equations and Optimal Control (2012), pp. 119-125. · Zbl 1291.35234
[179] N. Yu. Selivanova and M. V. Shamolin, “Local solvability of a one-phase problem with a free boundary,” in: Contemporary Mathematics and Its Applications [in Russian], 78, Partial Differential Equations and Optimal Control (2012), pp. 99-108. · Zbl 1302.35468
[180] Shamolin, MV, Closed trajectories of different topological type in the problem of the motion of a body in a medium with resistance, Vestn. MGU, Ser. 1, Mat., Mekh., 2, 52-56, (1992)
[181] Shamolin, MV, Problem of the motion of a body in a medium with resistance, Vestn. MGU, Ser. 1, Mat., Mekh., 1, 52-58, (1992) · Zbl 0753.70007
[182] Shamolin, MV, Classification of phase portraits in the problem of the motion of a body in a resisting medium under presence of a linear damping moment, Prikl. Mat. Mekh., 57, 40-49, (1993)
[183] M. V. Shamolin, “A new two-parameter family of phase portaits for problem of the motion of a body in a resisting medium,” in: Modelling and Study of Stability of Systems, Scientific Conference, May 24-28, 1993. Abstracts of Reports Pt. 2 [in Russian], Znanie, Kiev (1993), pp. 62-63.
[184] M. V. Shamolin, “Relative structural stability of the problem of the motion of a body in a resisting medium,” in: Mechanics and Its Applications, Scientific Conference, November 9-11, 1993, Abstracts of Reports [in Russian], Tashkent State University, Tashkent (1993), pp. 20-21.
[185] Shamolin, MV, Applications of Poincaré topographical system methods and comparison systems in some concrete systems of differential equations, Vestn. MGU, Ser. 1, Mat., Mekh., 2, 66-70, (1993)
[186] Shamolin, MV, Existence and uniqueness of trajectories having infinitely distant points as limit sets for dynamical systems on a plane, Vestn. MGU, Ser. 1, Mat., Mekh., 1, 68-71, (1993) · Zbl 0815.34002
[187] Shamolin, MV, A new two-parameter family of phase portraits in problem of the motion of a a body in a medium, Dokl. Ross. Akad. Nauk, 337, 611-614, (1994)
[188] M. V. Shamolin, “On relative roughness in the problem of the motion of a body in a medium under streamline flow,” in: Modelling and Study Stability of Systems, Scientific Conference, May 16-20, 1994. Abstract of Reports [in Russian], Kiev (1994), pp. 144-145. · Zbl 0205.54201
[189] M. V. Shamolin, “A new two-parameter family of phase portraits with limit cycles in the dynamics of a rigid body interacting with a medium,” in: Modelling and Study of Stability of Systems, Scientific Conference, May 15-19, 1995. Abstracts of Reports (Study of Systems) [in Russian], Kiev (1995), p. 125.
[190] M. V. Shamolin, “On relative stability of dynamical systems in the problem of the motion of a body in a resisting medium,” in: Abstracts of Reports of Chebyshev Readings, Vestn. VGU, Ser. 1, Mat., Mekh.,6, 17 (1995).
[191] M. V. Shamolin, “Relative structural stability of dynamical systems for the problem of the motion of a body in a medium,” in: Analytical, Numerical, and Experimental Methods in Mechanics. A Collection of Scientific Works [in Russian], MGU, Moscow (1995), pp. 14-19.
[192] Shamolin, MV, Introduction to problem of body drag in a resisting medium and a new twoparameter family of phase portraits, Vestn. MGU, Ser. 1, Mat., Mekh., 4, 57-69, (1996)
[193] M. V. Shamolin, “Introduction to spatial dynamics of rigid body motion in a resisting medium,” in: Materials of International Conference and Chebyshev Readings Devoted to the 175th Anniversary of P. L. Chebyshev, Moscow, May 14-19, 1996, Vol. 2 [in Russian], MGU, Moscow (1996), pp. 371-373.
[194] M. V. Shamolin, “Qualitative methods in dynamics of a rigid body interacting with a medium,” in: II Siberian Congress in Applied and Industrial Mathematics, Novosibirsk, June 25-30, 1996. Abstracts of Reports. Pt. III [in Russian], Novosibirsk (1996), p. 267.
[195] M. V. Shamolin, “Variety of types of phase portraits in dynamics of a rigid body interacting with a resisting medium,” Dokl. Ross. Akad. Nauk, 349, No. 2, 193-197.
[196] M. V. Shamolin, “On a certain integrable case in dynamics of spatial body motion in a resisting medium,” in: II Symposium in Classical and Celestial Mechanics. Abstracts of Reports. Velikie Luki, August 23-28, 1996 [in Russian], Moscow-Velikie Luki (1996), pp. 91-92.
[197] Shamolin, MV, Definition of relative roughness and two-parameter family of phase portraits in rigid body dynamics, Usp. Mat. Nauk, 51, 175-176, (1996)
[198] Shamolin, MV, Periodic and Poisson stable trajectories in problem of the motion of a body in a resisting medium, Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela, 2, 55-63, (1996)
[199] M. V. Shamolin, “Spatial Poincaré topographical systems and comparison systems,” in: Abstracts of Reports of Mathematical Conference ‘Erugin Readings’, Brest, May 14-16, 1996 [in Russian], Brest (1996), p. 107.
[200] M. V. Shamolin, “A list of integrals of dynamical equations in the spatial problem of the motion of a body in a resisting medium,” in: Modelling and Study of Stability of Systems, Scientific Conference, May 20-24, 1996. Abstracts of Reports (Study of Systems) [in Russian], Kiev (1996), p. 142.
[201] M. V. Shamolin, “Jacobi integrability of problem of a spatial pendulum placed in a flow of a medium,” in: Modelling and Study of Systems, Scientific Conference, May, 19-23, 1997. Abstracts of Reports [in Russian], Kiev (1997), p. 143.
[202] M. V. Shamolin, “Qualitative methods in dynamics of a rigid body interacting with a medium,“ in: YSTM96: ‘Young Peoples, the Third Millenium,’ Proceedings of International Congress (Ser. Professional) [in Russian], \(2\), NTA “APFN,” Moscow (1997), pp. I-4.
[203] M. V. Shamolin, “Mathematical modelling of dynamics of a spatial pendulum in a flow of a medium,” in: Proceedings of VII International Symposium ‘Methods of Discrete Singularities in Problems of Mathematical Physics,’ June 26-29, Feodociya [in Russian], Kherson State Technical University, Kherson (1997), pp. 153-154.
[204] Shamolin, MV, On an integrable case in spatial dynamics of a rigid body interacting with a medium, Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela, 2, 65-68, (1997)
[205] M. V. Shamolin, “Spatial dynamics of a rigid body interacting with a medium,” in: Workshop in Mechanics of Systems and Problems of Motion Control and Navigation, Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela, 4, 174 (1997).
[206] Shamolin, MV, Spatial Poincaré topographical systems and comparison systems, Usp. Mat. Nauk, 52, 177-178, (1997)
[207] M. V. Shamolin, “Partial stabilization of rotational motions of a body in a medium under free drag,” Abstracts of Reports of All-Russian Conference With International Participation ‘Problems of Celestial Mechanics,’ St.-Petersburg, June 3-6, 1997, Institute of Theoretical Astronomy [in Russian], Institute of Theoretical Astronomy, Russian Academy of Sciences, St.-Petersburg (1997), pp. 183-184.
[208] M. V. Shamolin, “Absolute and relative structural stability in spatial dynamics of a rigid body interacting with a medium,” in: Proceedings of International Conference ‘Mathematics in Inductry’, ICIM-98, Taganrog, June 29- July 03, 1998 [in Russian], Taganrog State Pedagogical Institute, Taganrog (1998), pp. 332-333.
[209] M. V. Shamolin, “Qualitative and numerical methods in some problems of spatial dynamics of a rigid body interacting with a medium,” in: Abstracts of Reports of 5th International Conference-Workshop ‘Engineering-Physical Problems of New Techniques,’ Moscow, May 19-22, 1998 [in Russian], Moscow State Technical University, Moscow (1998), pp. 154-155. · Zbl 1067.93020
[210] M. V. Shamolin, “Methods of nonlinear analysis in dynamics of a rigid body interacting with a medium,” in: Abstracts of Reports of International Conference ‘Nonlinear Analysis and Its Applications’ (Moscow, September 1-5, 1998) [in Russian], Moscow (1998), p. 131.
[211] M. V. Shamolin, “Some problems of spatial dynamics of a rigid body interacting with a medium under quasi-stationarity conditions,” in: Abstracts of Reports of All-Russian Scientific-Technical Conference of Young Scientists ‘Modern Problems of Aero-Cosmic Science,’ Zhukovskii, May 27-29, 1998 [in Russian], Central Aero-Hydrodynamical Institute, Moscow (1998), pp. 89-90.
[212] M. V. Shamolin, “Methods of nonlinear analysis in dynamics of a rigid body interacting with a medium,” in: CD-Proceedings of the Congress ‘Nonlinear Analysis and Its Applications’, Moscow, Russia, Sept. 1-5, 1998 [in Russian], Moscow (1999), pp. 497-508.
[213] Shamolin, MV, On integrability in transcendental functions, Usp. Mat. Nauk, 53, 209-210, (1998)
[214] M. V. Shamolin, “Families of three-dimensional phase portraits in spatial dynamics of a rigid body interacting with a medium,” in: III International Symposium in Classical and Celestial Mechanics, August 23-27, 1998, Velikie Luki. Abstracts of Reports [in Russian], Computational Center of Russian Academy of Sciences, Moscow-Velikie Luki (1998), pp. 165-167.
[215] Shamolin, MV, Families of portraits with limit cycles in plane dynamics of a rigid body interacting with a medium, Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela, 6, 29-37, (1998)
[216] Shamolin, MV, Certain classes of partial solutions in dynamics of a rigid body interacting with a medium, Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela, 2, 178-189, (1999)
[217] M. V. Shamolin, “Nonlinear dynamical effects in spatial body drag in a resisting medium,” in: Abstracts of Reports of III International Conference ‘Chkalov Readings, Engineering-Physical Problems of Aviation and Cosmic Technics’ (June 1-4, 1999) [in Russian], EATK GA, Egor’evsk (1999), pp. 257-258.
[218] Shamolin, MV, New Jacobi integrable cases in dynamics of a rigid body interacting with a medium, Dokl. Ross. Akad. Nauk, 364, 627-629, (1999) · Zbl 1065.70500
[219] M. V. Shamolin, “Families of long-period trajectories in spatial dynamics of a rigid body,” in: Modelling and Study of Stability of Systems, Scientific Conference, May 25-29 1999. Abstracts of Reports [in Russian], Kiev (1999), p. 60.
[220] Shamolin, MV, On roughness of dissipative systems and relative roughness and non-roughness of variable dissipation systems, Usp. Mat. Nauk, 54, 181-182, (1999)
[221] M. V. Shamolin, “Problem of the motion of a four-dimensional body in a resisting medium and one case of integrability,” in: Book of Abstracts of the Third International Conference ‘Differential Equations and Applications’, St.-Petersburg, Russia, June 12-17, 2000 [in Russian], St.-Petersburg State University, St.-Petersburg (2000), p. 198.
[222] Shamolin, MV, Jacobi integrability in problem of four-dimensional rigid body motion in a resisting medium, Dokl. Ross. Akad. Nauk, 375, 343-346, (2000)
[223] M. V. Shamolin, “Jacobi integrability of the problem of the motion of a four-dimensional body in a resisting medium,” in: Abstracts of Reports of International Conference in Differential Equations and Dynamical Systems, Suzdal’, August 21-26, 2000 [in Russian], Vladimir, Vladimir State University (2000), pp. 196-197. · Zbl 1189.70045
[224] M. V. Shamolin, “Many-dimensional Poincaré systems and transcendental integrability,” in: IV Siberian Congress in Applied and Industrial Mathematics, Novosibirsk, June 26-July 01, 2000. Abstracts of Reports, Pt. I. [in Russian], Novosibirsk, Institute of Mathematics (2000), pp. 25-26.
[225] Shamolin, MV, A new family of phase portraits in spatial dynamics of a rigid body interacting with a medium, Dokl. Ross. Akad. Nauk, 371, 480-483, (2000)
[226] M. V. Shamolin, “On a certain case of Jacobi integrability in dynamics of a four-dimensional rigid body interacting with a medium,” in: Abstracts of Reports of International Conference in Differential and Integral Equations, Odessa, September 12-14, 2000 [in Russian], AstroPrint, Odessa (2000), pp. 294-295.
[227] M. V. Shamolin, “On roughness of dissipative systems and relative roughness of variable dissipation systems,” in: Abstracts of Reports of P. K. Rashevskii Workshop in Vector and Tensor Analysis, Vestn. MGU, Ser. 1, Mat., Mekh., 2, 63 (2000).
[228] Shamolin, MV, On limit sets of differential equations near singular points, Usp. Mat. Nauk, 55, 187-188, (2000)
[229] M. V. Shamolin, “Comparison of certain integrability cases from two-, three-, and fourdimensional dynamics of a rigid body interacting with a medium,” in: Abstracts of Reports of V Crimean International Mathematical School ‘Lyapunov function Method and Its Application,’ (MLF-2000), Crimea, Alushta, September 5-13, 2000 [in Russian], Simpheropol’ (2000), p. 169.
[230] M. V. Shamolin, “Integrability of a problem of four-dimensional rigid body in a resisting medium,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Fund. Prikl. Mat.,7, No. 1, 309 (2001).
[231] M. V. Shamolin, “Variety of types of phase portraits in dynamics of a rigid body interacting with a medium,” in Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Fund. Prikl. Mat.,7, No. 1, 302-303 (2001). · Zbl 0205.54201
[232] M. V. Shamolin, “New Jacobi integrable cases in dynamics of two-, three-, and four-dimensional rigid body interacting with a medium,” Absracts of Reports of VIII All-Russian Congress in Theoretical and Applied Mechanics, Perm’, August 23-29, 2001 [in Russian], Ural Department of Russian Academy of Sciences, Ekaterinburg (2001), pp. 599-600.
[233] M. V. Shamolin, “New integrable cases in dynamics of a four-dimensional rigid body interacting with a medium,” in: Abstracts of Reports of Scientific Conference, May 22-25, 2001 [in Russian], Kiev (2001), p. 344.
[234] Shamolin, MV, On stability of motion of a body twisted around its longitudinal axis in a resisting medium, Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela, 1, 189-193, (2001)
[235] Shamolin, MV, Complete integrability of equations for motion of a spatial pendulum in a flow of a medium, Vestn. MGU, Ser. 1, Mat., Mekh., 5, 22-28, (2001)
[236] Shamolin, MV, Integrability cases of equations for spatial dynamics of a rigid body, Prikl. Mekh., 37, 74-82, (2001) · Zbl 1010.70520
[237] M. V. Shamolin, “New integrable cases in dynamics of a two-, three-, and four-dimensional rigid body interacting with a medium,” in: Abstracts of Reports of International Conference in Differential Equations and Dynamical Systems, Suzdal’, July 1-6, 2002 [in Russian], Vladimir State University, Vladimir (2002), pp. 142-144.
[238] Shamolin, MV, On integrability of certain classes of nonconservative systems, Usp. Mat. Nauk, 57, 169-170, (2002)
[239] M. V. Shamolin, “Integrability in transcendental functions in rigid body dynamics,” in: Abstracts of Reports of Scientific Conference ‘Lomonosov Readings,’ Sec. Mechanics, April 17-27, 2003, Moscow, M. V. Lomonosov Moscow State University [in Russian], MGU, Moscow (2003), p. 130.
[240] M. V. Shamolin, “On integrability of nonconservative dynamical systems in transcendental functions,” in: Modelling and Study of Stability of Systems, Scientific Conference, May 27-30, 2003, Abstracts of Reports [in Russian], Kiev (2003), p. 377.
[241] M. V. Shamolin, “On a certain spatial problem of rigid body motion in a resisting medium,” in: Abstracts of Reports of International Scientific Conference Third Polyakhov Readings,’ St.-Petersburg, February 4-6, 2003 [in Russian], NIIKh St.-Petersburg Univ, (2003), pp. 170-171.
[242] Shamolin, MV, Geometric representation of motion in a certain problem of body interaction with a medium, Prikl. Mekh., 40, 137-144, (2004) · Zbl 1116.74378
[243] M. V. Shamolin, “Variable dissipation dynamical systems in dynamics of a rigid body interacting with a medium,” in: Differential Equations and Computer Algebra Tools, Materials of International Conference, Brest, October 5-8, 2005, Pt. 1. [in Russian], BGPU, Minsk (2005), pp. 231-233.
[244] M. V. Shamolin, “Integrability in transcendental functions in rigid body dynamics,” in: Mathematical Conference ‘Modern Problems of Applied Mathematics and Mathematical Modelling,’ Voronezh, December 12-17, 2005 [in Russian], Voronezh State Academy, Voronezh (2005), p. 240.
[245] M. V. Shamolin, “Integrability of nonconservative systems in elementary functions,” in: X Academician M. Kravchuk Mathematical International Conference, September 3-15, 2004, Kiev [in Russian], Kiev (2004), p. 279.
[246] M. V. Shamolin, Some Problems of Differential and Topological Diagnosis [in Russian], Ekzamen, Moscow (2004).
[247] M. V. Shamolin, “On a certain integrable case in dynamics on so(4) \(×\) ℝ\^{}{4},” in: Abstracts of Reports of All-Russian Conference ‘Differential Equations and Their Applications,’ (SamDif-2005), Samara, June 27-July 2, 2005 [in Russian], Univers-Grupp, Samara (2005), pp. 97-98.
[248] Shamolin, MV, On a certain integrable case of equations of dynamics in so(4) × ℝ\^{}{4}, Usp. Mat. Nauk, 60, 233-234, (2005)
[249] M. V. Shamolin, “On the motion of a rigid body in a resisting medium with account for rotational derivatives of aerodynamical force moment in angular velocity,” in: Modelling and Studying of Systems, Scientific Conference, May 23-25, 2005. Abstracts of Reports [in Russian], Kiev (2005), p. 351.
[250] M. V. Shamolin, “On the motion of a body in a resisting medium with account for rotational derivatives of aerodynamical force moment in angular velocity,” in: Abstracts of Reports of Scientific Conference ‘Lomonosov Readings-2005,’ Sec. Mechanics, April, 2005, Moscow, M. V. Lomonosov Moscow State University [in Russian], MGU, Moscow (2005), p. 182.
[251] M. V. Shamolin, “Cases of complete integrability in dynamics of a four-dimensional rigid body interacting with a medium,” in: Abstracts of Reports of International Conference ‘Functional Spaces, Approximation Theory, and Nonlinear Analysis’ Devoted to the 100th Anniversary of A. M. Nikol’skii, Moscow, May 23-29, 2005 [in Russian], V. A. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow (2005), p. 244.
[252] Shamolin, MV, A case of complete integrability in spatial dynamics of a rigid body interacting with a medium with account for rotational derivatives of force moment in angular velocity, Dokl. Ross. Akad. Nauk, 403, 482-485, (2005)
[253] Shamolin, MV, Comparison of Jacobi integrable cases of plane and spatial body motions in a medium under streamline flow, Prikl. Mat. Mekh., 69, 1003-1010, (2005) · Zbl 1100.74546
[254] Shamolin, MV, Problem on rigid body spatial drag in a resisting medium, Izv. Ross. Akad. Nauk, Mekhanika Tverdogo Tela, 3, 45-57, (2006)
[255] M. V. Shamolin, “On the spatial problem of rigid body interaction with a resisting medium,” in: Abstracts of Reports of IX All-Russian Congress in Theoretical and Applied Mechanics, Nizhnii Novgorod, August 22-28, 2006. Vol. I [in Russian]. N. I. Lobachevskii Nizhegorodskii State Univesity, Niznii Novgorod (2006), p. 120.
[256] M. V. Shamolin, “Model problem of the motion of a body in a resisting medium with account for dependence of resistance force on angular velocity,” in: Scientifuc Report of Institute of Mechanics, Moscow State University [in Russian], No. 4818, Institute of Mechanics, Moscow State University, Moscow (2006).
[257] M. V. Shamolin, “On a case of complete integrability in four-dimensional rigid body dynamics,” Abstracts of Reports of International Conference in Differential Equations and Dynamical Systems, Vladimir, July 10-15, 2006 [in Russian], Vladimir State University, Vladimir (2006), pp. 226-228.
[258] M. V. Shamolin, “On trajectories of characteristic points of a rigid body moving in a medium,” in: International Conference ‘Fifth Okunev Readings,’ St.-Petersburg, June 26-30, 2006. Abstracts of Reports [in Russian], Balt. State Technical University, St. Petersburg (2006), p. 34.
[259] M. V. Shamolin, “Spatial problem on the motion of a rigid body in a resisting medium,” in: VIII Crimean International Mathematical School ‘Lyapunov Function Method and Its Applications,’ Abstracts of Reports, Alushta, September 10-17, 2006, Tavriya National University [in Russian], DiAiPi, Simpheropol’ (2006), p. 184.
[260] M. V. Shamolin, “Variable dissipation systems in dynamics of the interacting of a rigid body with a medium,” Fourth Polyakhov Readings, Abstracts of Reports of International Scientific Conference in Mechanics, St.-Petersburg, February 7-10, 2006 [in Russian], VVM, St.-Petersburg (2006), p. 86.
[261] M. V. Shamolin, “On account of rotational derivatives of an aerodynamical force moment on the motion of a body in a resisting medium,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Contemporary Mathematics, Fundamental Directions [in Russian], 23 (2007), p. 44.
[262] M. V. Shamolin, “Integrability in elementary functions of variable dissipation systems,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Contemporary Mathematics, Fundamental Directions [in Russian], 23 (2007), p. 38.
[263] M. V. Shamolin, “Integrability of problem of the motion of a four-dimensional rigid body in a resisting medium,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Contemporary Mathematics, Fundamental Directions [in Russian], 23 (2007), p. 21.
[264] M. V. Shamolin, “Integrability of strongly nonconservative systems in transcendental elementary functions,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Contemporary Mathematics, Fundamental Directions [in Russian], 23 (2007), p. 40.
[265] M. V. Shamolin, Methods for Analysis of Variable-Dissipation Dynamical Systems in Rigid Body Dynamics [in Russian], Ekzamen, Moscow (2007). · Zbl 1334.70001
[266] M. V. Shamolin, “Variety of types of phase portraits in dynamics of a rigid body interacting with a medium,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Contemporary Mathematics, Fundamental Directions [in Russian], 23 (2007), p. 17.
[267] M. V. Shamolin, Some Problems of Differential and Topological Diagnosis [in Russian], 2nd Corrected and Enlarged Edition, Ekzamen, Moscow (2007).
[268] Shamolin, MV, Some model problems of dynamics for a rigid body interacting with a medium, Prikl. Mekh., 43, 49-67, (2007) · Zbl 1164.74395
[269] M. V. Shamolin, “New integrable cases in dynamics of a four-dimensional rigid body interacting with a medium,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Contemporary Mathematics, Fundamental Directions [in Russian], 23 (2007), p. 27.
[270] M. V. Shamolin, “On integrability in transcendental functions,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Contemporary Mathematics, Fundamental Directions [in Russian], 23, (2007), p. 34.
[271] M. V. Shamolin, “On integrability in elementary functions of certain classes of nonconservative dynamical systems,” in: Modelling and Study of Systems, Scientific Conference, May 22-25, 2007. Abstracts of Reports [in Russian], Kiev (2007), p. 249.
[272] M. V. Shamolin, “On integrability of motion of four-dimensional body-pendulum situated in a flow of a medium,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Contemporary Mathematics, Fundamental Directions [in Russian], 23 (2007), p. 37. · Zbl 1212.70023
[273] M. V. Shamolin, “On stability of a certain regime of rigid body motion in a resisting medium,” in: Abstracts of Reports of Scientific Conference ‘Lomonosov Readings-2007,’ Sec. Mechanics, Moscow, Moscow State University, April, 2007 [in Russian], MGU, Moscow (2007), p. 153.
[274] M. V. Shamolin, “On account of rotational derivatives of aerodynamical force moment on body motion in a resisting medium,” in: Abstracts of Session of Workshop ‘Actual Problems of Geometry and Mechanics,’ Contemporary Problems in Mathematics, Fundamental Directions [in Russian], 23, Moscow (2007), p. 26.
[275] M. V. Shamolin, “On rigid body motion in a resisting medium taking account of rotational derivatives of aerodynamical force moment in angular velocity,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics,’ Contemporary Mathematics, Fundamental Directions [in Russian], 23 (2007), p. 44.
[276] Shamolin, MV, Complete integrability of equations of motion for a spatial pendulum in a flowing medium taking account of rotational derivatives of moments of its action force, Izv. Ross Akad. Nauk, Mekhanika Tverdogo Tela, 3, 187-192, (2007)
[277] M. V. Shamolin, “Cases of complete integrability in dynamics of a rigid body interacting with a medium,” Abstracts of Reports of All-Russiann Conference ‘Modern Problems of Contionuous Medium Mechanics’ Devoted to the Memory of L. I. Sedov in Connection With His 100th Anniversary, Moscow, November, 12-14, 2007 [in Russian], MIAN, Moscow (2007), pp. 166-167.
[278] M. V. Shamolin, “Cases of complete integrability in dynamics of a four-dimensional rigid body in a nonconservative force field,” in: Abstract of Reports of International Conference ‘Analysis and Singularities,’ Devoted to 70th Anniversary of V. I. Arnol’d, August 20-24, 2007, Moscow [in Russian], MIAN, Moscow (2007), pp. 110-112.
[279] M. V. Shamolin, “Cases of complete integrability in elementary functions of certain classes of nonconservative dynamical systems,” in: Abstracts of Reports of International Conference ‘Classical Problems of Rigid Body Dynamics,’ June 9-13, 2007 [in Russian], Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (2007), pp. 81-82.
[280] M. V. Shamolin, “Case of complete integrability in dynamics of a four-dimensional rigid body in nonconservative force field,” in: ‘Nonlinear Dynamical Analysis-2007,’ Abstracts of Reports of International Congress, St. Petersburg, June 4-8, 2007 [in Russian], St.-Petersburg State University, St.-Petersburg (2007), p. 178.
[281] Shamolin, MV, A case of complete integrability in dynamics on a tangent bundle of twodimensional sphere, Usp. Mat. Nauk, 62, 169-170, (2007)
[282] Shamolin, MV, Dynamical systems with variable dissipation: approaches, methods, and applications, Fund. Prikl. Mat., 14, 3-237, (2008)
[283] M. V. Shamolin, “Qualitative methods of analysis of variable dissipation systems in Dynamics,” in: International Conference ‘Sixth Okunev Readings,’ St.-Petersburg, June 23-27, 2008. Materials of Reports, Vol. III [in Russian], Balt. State Technical University, St.-Petersburg (2008), pp. 34-39.
[284] M. V. Shamolin, “Methods of analysis of dynamical systems with sign-variable dissipation,” in: Abstracts of Reports of International Conference in Differential Equations and Dynamical Systems, Suzdal’, June 26-July 2, 2008 [in Russian], Vladimir, Vladimir State University (2008), pp. 259-260.
[285] M. V. Shamolin, “Methods of analysis of dynamical systems with certain group of symmetry,” in: Abstracts of Reports of International Conference ‘Differential Geometry and Topology’ in Honor of 100th Birthday of L. S. Pontryagin, Moscow, June 17-22, 2008, Faculty of VMK at MSU, Paks-Press, Moscow (2008), pp. 208-209.
[286] M. V. Shamolin, “Comparison of certain integrability cases from two-, three-, and fourdimensional dynamics of a rigid body interacting with a medium,” in: Abstracts of Reports of IX Crimean International Mathematical School ‘Lyapunov Function Method and Its Application,’ Crimea, Alushta, September 15-20, 2008 [in Russian], Simpheropol’ (2008), pp. 181-182.
[287] Shamolin, MV, New integrable cases in dynamics of a body interacting with a medium with allowance for dependence of resistance force moment on angular velocity, Prikl. Mat. Mekh., 72, 273-287, (2008) · Zbl 1189.70045
[288] M. V. Shamolin, “New cases of complete integrability in dynamics of symmetric four-dimensional rigid body in nonconservative field,” in: Materials of International Conference ‘Contemporary Problems of Mathematics, Mechanics, and Informatics’ in Honor of 85th Birthday of L. A. Tolokonnikov, Tula, Russia, November 17-21, 2008 [in Russian], Grif and Ko., Moscow (2008), pp. 317-320.
[289] M. V. Shamolin, “New integrable case in dynamics of four-dimensional rigid body in nonconservative field of forces,” in: Materials of Voronezh Spring Mathematical School ‘Pontryagin Readings-XIX,’ Voronezh, May, 2008 [in Russian], Voronezh State University, Voronezh (2008), pp. 231-232.
[290] Shamolin, MV, Integrability of some classes of dynamical systems in terms of elementary functions, Vestn. MGU, Ser. 1, Mat., Mekh., 3, 43-49, (2008) · Zbl 1212.70011
[291] M. V. Shamolin, “Systems with sign-variable dissipation in dynamics of a rigid body interacting with a medium,” in: Abstracts of Reports of Scientific Conference ‘Lomonosov Readings,’ Sec. Mechanics, April, 2008, Moscow, M. V. Lomonosov Moscow State University [in Russian], MGU, Moscow (2008), pp. 159-160.
[292] Shamolin, MV, Three-parameter family of phase portraits in dynamics of a solid interacting with a medium, Dokl. Ross. Akad. Nauk, 418, 46-51, (2008)
[293] Shamolin, MV, Diagnosis of failures in certain non-direct control system, Elektronnoe Modelirovanie, 31, 55-66, (2009)
[294] M. V. Shamolin, “Classification of complete integrability cases in four-dimensional symmetric rigid-body dynamics in a nonconservative field,” in: Contemporary Mathematics and Its Applications [in Russian], 65, Mathematical Physics, Combinatorics, and Optimal Control (2009), pp. 132-142.
[295] M. V. Shamolin, “Methods for analysis of various dissipation dynamical systems,” in: Abstract of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics’, Contemporary athematics and Its Applications [in Russian], 62, Geometry and Mechanics (2009), p. 13.
[296] M. V. Shamolin, “New cases of integrability in dynamics of four-dimensional rigid body in a nonconservative field,” in: Abstract of sessions of workshop ‘Actual Problems of Geometry and Mechanics’, Contemporary Mathematics and Its Applications [in Russian], 65, Mathematical Physics, Combinatorics, and Optimal Control (2009), p. 6.
[297] M. V. Shamolin, “Certain cases of complete integrability in spatial dynamics of a rigid body interacting with a medium,” in: Abstracts of Reports of International Scientific Conference Fifth Polyakhov Readings,’ St.-Petersburg, February 3-6, 2009 [in Russian], St.-Petersburg Univ (2009), p. 73.
[298] M. V. Shamolin, “Certain cases of complete integrability in spatial dynamics of a rigid body interacting with a medium,” in: Proc. of International Scientific Conference Fifth Polyakhov Readings,’ St.-Petersburg, February 3-6, 2009 [in Russian], St.-Petersburg Univ, (2009), pp. 144-150.
[299] Shamolin, MV, New cases of full integrability in dynamics of a dynamically symmetric fourdimensional solid in a nonconservative field, Dokl. Ross. Akad. Nauk, 425, 338-342, (2009)
[300] M. V. Shamolin, “New cases of complete integrability in spatial dynamics of a rigid body interacting with a medium,” in: Abstracts of Reports of Scientific Conference ‘Lomonosov Readings,’ Sec. Mechanics, April, 2009, Moscow, M. V. Lomonosov Moscow State University [in Russian], MGU, Moscow (2009), pp. 153-154. · Zbl 1274.74112
[301] M. V. Shamolin, “On integrability in terms of transcendental functions in dynamics of a rigid body interacting with a medium,” in: Materials of Voronezh Spring Mathematical School ‘Pontryagin Readings-XX,’ Voronezh, May 3-9, 2009 [in Russian], Voronezh State University, Voronezh (2009), pp. 191-192.
[302] M. V. Shamolin, “On integrability in elementary functions of certain classes of nonconservative dynamical systems,” in: Contemporary Mathematics and Its Applications. [in Russian], 62, Geometry and Mechanics (2009), pp. 131-171. · Zbl 1188.37003
[303] M. V. Shamolin, “On integrability of certain classes of dynamical systems,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics’, Contemporary Mathematics and Its Applications [in Russian], 62, Geometry and Mechanics (2009), p. 10.
[304] M. V. Shamolin, “On stability of certain conditions of rigid body motion in a resisting medium,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics’, Contemporary Mathematics and Its Applications [in Russian], 62, Geometry and Mechanics (2009), pp. 10-11.
[305] Shamolin, MV, Stability of rectilinear translational motion, Prikl. Mekh., 45, 125-140, (2009) · Zbl 1212.70023
[306] M. V. Shamolin, “On trajectories diverging to infinity for planar dynamical systems,” in: Abstract of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics’, Contemporary Mathematics and Its Applications [in Russian], 62, Geometry and Mechanics (2009), p. 7.
[307] Shamolin, MV, Generalized problem of differential diagnosis and its possible solution, Elektronnoe Modelirovanie, 31, 97-115, (2009)
[308] Shamolin, MV, Solution of diagnosis problem in case of precise trajectory measurements with error, Elektronnoe Modelirovanie, 31, 73-90, (2009)
[309] M. V. Shamolin, “Variable dissipation systems: methods, approaches, and applications,” in: Abstracts of Reports of Scientific Conference, May 27-29, 2009 [in Russian], Kiev (2009), p. 163.
[310] M. V. Shamolin, “Cases of integrability of equations of motion of a four-dimensional rigid body in a nonconservative field of forces,” in: Materials of International Conference ‘Contemporary Problems in Mathematics, Mechanics, and Its Applications’ Devoted to the 70th Anniversary of V. A. Sadovnichii, Moscow, March 30-April 2, 2009 [in Russian], Universitetskaya Kniga, Moscow (2009), p. 233. · Zbl 1347.70010
[311] M. V. Shamolin, “Case of complete integrability in Dynamics of symmetric four-dimensional rigid body in a nonconservative field,” in: Abstract of sessions of workshop ‘Actual Problems of Geometry and Mechanics’, Contemporary Mathematics and Its Applications [in Russian], 65, Mathematical Physics, Combinatorics, and Optimal Control (2009), p. 9.
[312] Shamolin, MV, Motion diagnosis of aircraft in mode of planned descent, Elektronnoe Modelirovanie, 32, 31-44, (2010)
[313] Shamolin, MV, Diagnosis of a system of direct control of aircraft motion, Elektronnoe Modelirovanie, 32, 45-52, (2010)
[314] M. V. Shamolin, “Integrability and non-integrability of dynamical systems in transcendental functions,” in: Abstracts of Reports of Voronezh Winter Mathematical School of S. G. Kreyn, Voronez, 2010 [in Russian], Voronezh State University, Voronezh (2010), pp. 159-160.
[315] M. V. Shamolin, “On the problem of the motion of the body with front flat butt end in a resisting medium,” in: Scientific Report of Institute of Mechamics, Moscow State University [in Russian], No. 5052, Institute of Mechanics, Moscow State University, Moscow (2010).
[316] Shamolin, MV, New cases of integrability in the spatial dynamics of a rigid body, Dokl. Ross. Akad. Nauk, 431, 339-343, (2010)
[317] Shamolin, MV, Spatial motion of a rigid body in a resisting medium, Prikl. Mekh., 46, 120-133, (2010)
[318] M. V. Shamolin, “Cases of complete integrability of the equations of motion of a dynamicalsymmetric four-dimensional rigid body in a nonconservative field,” in: Abstracts of Reports of International Conference in Differential Equations and Dynamical Systems, Suzdal’, July 2-7, 2010 [in Russian], Vladimir, Vladimir State University (2010), p. 195. · Zbl 1288.70001
[319] M. V. Shamolin, “Cases of complete integrability of the spatial motion equations of a rigid body in a resisting medium,” in: Abstracts of Reports of XI International Conference ‘ Stability and Oscillations of Nonlinear Control Systems,’ Moscow, IPU RAN, June 1-4, 2010 [in Russian], Moscow, IPU RAN (2010), pp. 429-431.
[320] M. V. Shamolin, “Cases of complete integrability of spatial dynamics equations of a rigid body in a resisting medium,” in: Abstracts of Reports of Scientific Conference ‘Lomonosov Readings,’ Sec. Mechanics, April, 2010, Moscow , M. V. Lomonosov Moscow State University [in Russian], MGU, Moscow (2010), p. 172.
[321] Shamolin, MV, A completely integrable case in the dynamics of a four-dimensional rigid body in a non-conservative field, Usp. Mat. Nauk, 65, 189-190, (2010)
[322] Shamolin, MV, Rigid body motion in a resisting medium, Matem. Mod., 23, 79-104, (2011) · Zbl 1274.74112
[323] Shamolin, MV, Diagnosis of gyro-stabilized platform included in control system of aircraft motion, Elektronnoe Modelirovanie, 33, 121-126, (2011)
[324] Shamolin, MV, Dynamical invariants of integrable variable dissipation dynamical systems, Vestnik Nizhegorod. Univ., 2, 356-357, (2011)
[325] Shamolin, MV, A multiparameter family of phase portraits in the dynamics of a rigid body interacting with a medium, Vestn. MGU, Ser. 1, Mat., Mekh., 3, 24-30, (2011)
[326] Shamolin, MV, A new case of integrability in dynamics of a 4D-solid in a nonconservative field, Dokl. Ross. Akad. Nauk, 437, 190-193, (2011)
[327] M. V. Shamolin, “New case of complete integrability of the dynamical equations on the tangential stratification of three-dimensional sphere,” in: Vestnik SamGU. Natural Sciences, No. 5(86), 187-189, (2011).
[328] M. V. Shamolin, “Complete lists of first integrals in dynamics of four-dimensional rigid body in a nonconservative force,” in: Abstracts of Reports of International Conference Devoted to 110th Anniversary of I. G. Petrovskii, 2011, Moscow [in Russian], MGU and ‘Intuit. RU’, Moscow (2011), pp. 389-390.
[329] Shamolin, MV, Complete List of first integrals in the problem on the motion of a 4D solid in a resisting medium under assumption of linear damping, Dokl. Ross. Akad. Nauk, 440, 187-190, (2011)
[330] M. V. Shamolin, “Comparison of complete integrability cases from two-, three-, and fourdimensional dynamics of a rigid body in a nonconservative field,” in: Abstracts of Reports of Scientific Conference ‘Dynamical System Modelling and Stability Investigation’, May 25-27, 2011 [in Russian], Kiev (2011), p. 139.
[331] Shamolin, MV, The problem of a rigid body motion in a resisting medium with the assumption of dependence of the force moment on the angular velocity, Matem. Mod., 24, 109-132, (2012) · Zbl 1289.70008
[332] M. V. Shamolin, “Variety of cases of integrability in rigid body dynamics in a nonconservative field,” in: Abstracts of Reports of Scientific Conference ‘Lomonosov Readings,’ Sec. Mechanics, April, 2012, Moscow, M. V. Lomonosov Moscow State University [in Russian], MGU, Moscow (2012), p. 156.
[333] M. V. Shamolin, “Some questions of qualitative theory in dynamics of systems with the variable dissipation,” in: Contemporary Mathematics and Its Applications [in Russian], 78, Partial Differential Equations and Optimal Control (2012), pp. 138-147.
[334] M. V. Shamolin, “New cases of integrability in transcendental functions in rigid body dynamics in a nonconservative field,” in: Materials of Voronezh Spring Mathematical School ‘Pontryagin Readings-XXIII,’ Voronezh, May 3-9, 2012 [in Russian], Voronezh State University, Voronezh (2012), p. 200. · Zbl 1277.37104
[335] Shamolin, MV, A new case of integrability in the dynamics of a 4D-rigid body in a nonconservative field under the assumption of linear damping, Dokl. Ross. Akad. Nauk, 444, 506-509, (2012)
[336] Shamolin, MV, A new case of integrability in spatial dynamics of a rigid solid interacting with a medium under assumption of linear damping, Dokl. Ross. Akad. Nauk, 442, 479-481, (2012)
[337] M. V. Shamolin, “New case of integrability in transcendental functions in dynamics of a rigid body interacting with a medium,” in: Abstracts of Reports of XII International Conference ‘Stability and Oscillations of Nonlinear Control Systems,’ Moscow, IPU RAN, June 5-8, 2012 [in Russian], Moscow, IPU RAN (2012), pp. 339-341.
[338] M. V. Shamolin, “Review of cases of integrability in dynamics of small- and multi-dimensional rigid body in a nonconservative field,” in: Abstracts of Reports of International Conference in Differential Equations and Dynamical Systems, Suzdal’, June 26-July 4, 2012 [in Russian], Suzdal’, Kollektiv Avtorov (2012), pp. 179-180.
[339] Shamolin, MV, Complete List of first integrals of dynamical equations of the spatial motion of a rigid body in a resisting medium under assumption of linear damping, Vestn. MGU, Ser. 1, Mat., Mekh., 4, 44-47, (2012)
[340] M. V. Shamolin, “Systems with variable dissipation: Methods, approaches, and applications,” in: Abstracts of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics’, Contemporary Mathematics and Its Applications [in Russian], 76, Geometry and Mechanics (2012), p. 6.
[341] M. V. Shamolin, “Cases of integrability in dynamics of four-dimensional rigid body in a nonconservative field,” in: Materials of Voronezh Winter Mathematical School of S. G. Kreyn, Voronez, January 25-30, 2012 [in Russian], Voronezh State University, Voronezh (2012), pp. 213-215. · Zbl 1277.37104
[342] M. V. Shamolin, “Cases of integrability in spatial dynamics of a rigid body in a medium in a jet flow,” in: Abstracts of Reports of International Scientific Conference ‘Sixth Polyakhov Readings,’ St.-Petersburg, January 31-February 3, 2012 [in Russian], I. V. Balabanov Publisher, St.-Petersburg (2012), p. 75.
[343] M. V. Shamolin, “Cases of integrability in spatial dynamics of a rigid body interacting with a medium under assumption of linear damping,” in: Proc. of X International Chetaev Conference ‘Analytical Mechanics, Stability and Control,’ Kazan’, Russia, June 12-16, 2012 [in Russian], Kazan’ State Technical University, Kazan’ (2012), pp. 508-514.
[344] M. V. Shamolin, “Cases of complete integrability in transcendental functions in Dynamics of a rigid body interacting with a medium,” in: Abstract of Sessions of Workshop ‘Actual Problems of Geometry and Mechanics’, Contemporary Mathematics and Its Applications [in Russian], 76, Geometry and Mechanics (2012), p. 7.
[345] M. V. Shamolin, “Comparison of complete integrability cases in dynamics of a two-, three-, and four-dimensional rigid body in a nonconservative field,” in: Contemporary Mathematics and Its Applications [in Russian], 76, Geometry and Mechanics (2012), pp. 84-99. · Zbl 1277.37104
[346] M. V. Shamolin and S. V. Tsyptsyn, “Analytical and numerical study of trajectories of the motion of a body in a resisting medium,” in: Scientific Report of Institute of Mechanivs, Moscow State University [in Russian], No. 4289, Institute ofMechanics, Moscow State University, Moscow (1993).
[347] M. V. Shamolin, “Global qualitative analysis of the nonlinear systems on the problem of the motion of a body in a resisting medium,” in: Fourth Colloquium on the Qualitative Theory of Differential Equations, Bolyai Institute, August 18-21, 1993, Szeged, Hungary (1993), p. 54. · Zbl 0820.76018
[348] M. V. Shamolin, “Relative structural stability on the problem of the motion of a body in a resisting medium,” in: ICM’94, Abstract of Short Communications, Zurich, 3-11 August, 1994, Zurich, Switzerland (1994), p. 207.
[349] M. V. Shamolin, “New two-parameter families of the phase patterns on the problem of the motion of a body in a resisting medium,” in: ICIAM’95, Book of Abstracts, Hamburg, 3-7 July, 1995, Hamburg, Germany (1995), p. 436.
[350] M. V. Shamolin, “Qualitative methods to the dynamical model of an interaction of a rigid body with a resisting medium and new two-parameter families of the phase portraits,” in: DynDays’95 (Sixteenth Annual Informal Workshop), Program and Abstracts, Lyon, June 28-July 1, 1995, Lyon, France (1995), p. 185.
[351] M. V. Shamolin, “Poisson-stable and dense orbits in rigid body dynamics,” in: 3rd Experimental Chaos Conference, Advance Program, Edinburg, Scotland, August 21-23, 1995, Edinburg, Scotland (1995), p. 114.
[352] M. V. Shamolin, “Structural optimization of the controlled rigid motion in a resisting medium,” in: WCSMO-1, Extended Abstracts. Posters, Goslar, May 28-June 2, 1995, Goslar, Germany (1995), pp. 18-19.
[353] M. V. Shamolin, “Qualitative methods in interacting with the medium rigid body dynamics,” in: Abstracts of GAMM Wissenschaftliche Jahrestangung’96, 27-31 May, 1996, Prague, Czech Rep., Karls-Universit¨at Prague (1996), pp. 129-130.
[354] M. V. Shamolin, “Qualitative methods in interacting with the medium rigid body dynamics, in: Abstracts of XIXth ICTAM, Kyoto, Japan, August 25-31, 1996, Kyoto, Japan (1996), p. 285.
[355] M. V. Shamolin, “Relative structural stability and relative structural instability of different degrees in topological dynamics,” in: Abstracts of International Topological Conference Dedicated to P. S. Alexandroff’s 100th Birthday ‘Topology and Applications’, Moscow, May 27-31, 1996, Phasys, Moscow (1996), pp. 207-208.
[356] M. V. Shamolin, “Topographical Poincaré systems in many dimensional spaces,” in: Fifth Colloquium on the Qualitative Theory of Differential Equations, Bolyai Institute, Regional Committee of the Hungarian Academy of Sciences, July 29-August 2, 1996, Szeged, Hungary (1996), p. 45.
[357] M. V. Shamolin, “Classical problem of a three-dimensional motion of a pendulum in a jet flow,” in: 3rd EUROMECH Solid Mechanics Conference, Book of Abstracts, Stockholm, Sweden, August 18-22, 1997, Royal Inst. of Technology, Stockholm, Sweden (1997), p. 204. · Zbl 0153.40901
[358] M. V. Shamolin, “Families of three-dimensional phase portraits in dynamics of a rigid body,” in: EQUADIFF 9, Abstracts, Enlarged Abstracts, Brno, Czech Rep., August 25-29, 1997, Masaryk Univ., Brno, Czech Rep. (1997), p. 76.
[359] M. V. Shamolin, “Three-dimensional structural optimization of controlled rigid motion in a resisting medium,” in: Proceedings of WCSMO-2, Zakopane, Poland, May 26-30, 1997, Zakopane, Poland (1997), p. 387-392. · Zbl 0084.08403
[360] M. V. Shamolin, “Three-dimensional structural optimization of controlled rigid motion in a resisting medium,” in: WCSMO-2, Extended Abstracts, Zakopane, Poland, May 26-30, 1997, Zakopane, Poland (1997), pp. 276-277.
[361] M. V. Shamolin, “Lyapunov functions method and many-dimensional topographical Poincaré systems in rigid body dynamics,” in: Abstracts of Reports of IV Crimean International Mathematical School ‘Lyapunov Function Method and Its Application,’ Crimea, Alushta, September 5-12, 1998 [in Russian], Simpheropol’ State University (1998), p. 80.
[362] M. V. Shamolin, “Many-dimensional topographical Poincaré systems in rigid body dynamics,” in: Abstracts of GAMM Wissenschaftliche Jahrestangung’98, 6-9 April, 1998, Bremen, Germany, Universitat Bremen (1998), p. 128.
[363] M. V. Shamolin, “New two-parameter families of the phase portraits in three-dimensional rigid body dynamics,” in: Abstracts of Reports of International Conference Dedicated to 90th Anniversary of L. S. Pontryagin, Moscow, August 31-September 6, 1998, Sect. Differential Equations [in Russian], MGU, Moscow (1998), pp. 97-99.
[364] M. V. Shamolin, “Some classical problems in a three dimensional dynamics of a rigid body interacting with a medium,” in: Proc. of ICTACEM’98, Kharagpur, India, Dec.1-5, 1998, Aerospace Engineering Dep., Indian Inst. of Technology, Kharagpur, India (1998), 11 p.
[365] M. V. Shamolin, “Integrability in terms of transcendental functions in rigid body dynamics,” in: Abstracts of GAMM Annual Meeting, April 12-16 1999, Metz, France, Universite de Metz (1999), p. 144.
[366] M. V. Shamolin, “Long-periodic trajectories in rigid body dynamics,” in: Sixth Colloquium on the Qualitative Theory of Differential Equations, Bolyai Institute, Regional Committee of the Hungarian Academy of Sciences, August 10-14, 1999, Szeged, Hungary (1999), p. 47.
[367] M. V. Shamolin, “Mathematical modelling in 3D dynamics of a rigid body interacting with a medium,“ in: Book of Abstracts of the Second Int. Conf. “Tools for Mathematical Modelling,” St.-Petersburg, Russia, 14-19 June, 1999, St.-Petersburg State Tech. Univ. (1999), pp. 122-123.
[368] M. V. Shamolin, “Methods of analysis of a deceleration of a rigid in 3D medium,” in: Contributed abstracts of 3rd ENOC, Copenhagen (Lyngby), Denmark, August 8-12, 1999, Tech. Univ. of Denmark (1999).
[369] M. V. Shamolin, “New families of the non-equivalent phase portraits in 3D rigid body dynamics,” in: Abstracts of Second Congress ISAAC 1999, Fukuoka, Japan, August 16-21, 1999, Fukuoka Ins. of Tech (1999), pp. 205-206.
[370] M. V. Shamolin, “Properties of integrability of systems in terms of transcendental functions,” in: Final Progr. and Abstracts of Fifth SIAM Conf. on Appl. of Dynamic. Syst., May 23-27, 1999, Snowbird, Utah, USA, SIAM (1999), p. 60.
[371] M. V. Shamolin, “Some properties of transcendental integrable dynamical systems,” in: Book of Abst. of EQUADIFF 10, Berlin, August 1-7, 1999, Free Univ. of Berlin (1999), p. 286-287.
[372] M. V. Shamolin, “Structural stability in 3D dynamics of a rigid body,” in: CD-Proc. of WCSMO-3, Buffalo, NY, May 17-21, 1999, Buffalo, NY (1999).
[373] M. V. Shamolin, Structural stability in 3D dynamics of a rigid body,” In: WCSMO-3, Short Paper Proc., vol. 2, Buffalo, NY, May 17-21, 1999, State Univ. of NY at Buffalo (1999), p. 475-477.
[374] M. V. Shamolin, “About interaction of a rigid body with a resisting medium under an assumption of a jet flow,” in: Book of Abst. II (General sessions) of 4th EUROMECH Solid Mech. Conf., Metz, France (June 26-30, 2000), Univ. of Metz (2000), p. 703.
[375] M. V. Shamolin, “Integrability and non-integrability in terms of transcendental functions,” in: CD-abs. of 3rd ECM (Poster sessions), Barcelona, Spain, June 10-14 (2000) (poster No. 36).
[376] M. V. Shamolin, “Mathematical modelling of interaction of a rigid body with a medium and new cases of integrability,” in: Book of Abst. of ECCOMAS 2000, Barcelona, Spain, 11-14 September, Barcelona (2000), p. 495.
[377] M. V. Shamolin, “Mathematical modelling of interaction of a rigid body with a medium and new cases of integrability,” in: CD-Proc. of ECCOMAS 2000, Barcelona, Spain, 11-14 September, Barcelona (2000).
[378] M. V. Shamolin, “Methods of analysis of dynamics of a rigid body interacting with a medium,” in: Book of Abstracts of Annual Scient. Conf. GAMM 2000 at the Univ. of G¨ottingen, 2-7 April, 2000, Univ. of G¨ott. (2000), p. 144.
[379] M. V. Shamolin, “New families of many-dimensional phase portraits in dynamics of a rigid body interacting with a medium,” in: Book of Abs. of 16th IMACS World Cong. 2000, Lausanne, Switzerland, August 21-25, EPFL (2000), p. 283.
[380] M. V. Shamolin, “New families of many-dimensional phase portraits in dynamics of a rigid body interacting with a medium,” in: CD-Proc. of 16th IMACS World Cong. 2000, Lausanne, Switzerland, August 21-25, EPFL (2000), 3 p.
[381] M. V. Shamolin, “Comparison of some cases of integrability in dynamics of a rigid body interacting with a medium,” in: Book of Abs. of Annual Scient. Conf. GAMM 2001, ETH Zurich, 12-15 February, 2001, ETH Zurich (2001), p. 132.
[382] M. V. Shamolin, “Pattern recognition in the model of the interaction of a rigid body with a resisting medium,” in: Col. of Abst. of First SIAM-EMS Conf. ‘Applied Mathematics in our Changing World’, Berlin, Germany, Sept. 2-6, 2001, Birkhauser, Springer (2001), p. 66.
[383] M. V. Shamolin, “Foundations in diferential and topological diagnostics,” in: Book of Abs. of Annual Scient. Conf. GAMM 2002, Univ. of Augsburg, March 25-28, 2002, Univ. of Augsburg (2002), p. 154.
[384] M. V. Shamolin, “Dynamical systems with the variable dissipation in 3D dynamics of a rigid body interacting with a medium,” in: Book of abstracts of 4th ENOC, Moscow, Russia, August 19-23, 2002 [in Russian], Moscow, Inst. Probl. Mech. Russ. Acad. Sci. (2002), p. 109.
[385] M. V. Shamolin, “Methods of analysis of dynamics of a 2D- 3D- or 4D-rigid body with a medium,” in: Abst. Short Commun. Post. Sess. Of ICM’2002, Beijing, 2002, August 20-28, Higher Education Press, Beijing, China, p. 268.
[386] Shamolin, MV, Some questions of the qualitative theory of ordinary differential equations and dynamics of a rigid body interacting with a medium, J. Math. Sci., 110, 2526-2555, (2002)
[387] Shamolin, MV, Foundations of differential and topological diagnostics, J. Math. Sci., 114, 976-1024, (2003) · Zbl 1067.93020
[388] M. V. Shamolin, “Global structural stability in dynamics of a rigid body interacting with a medium,” in: 5th ICIAM, Sydney, Australia, 7-11 July, 2003, Univ. of. Technology, Sydney (2003), p. 306.
[389] M. V. Shamolin, “Integrability and nonintegrability in terms of transcendental functions,” in: Book of Abs. of Annual Scient. Conf. GAMM 2003, Abano Terme-Padua, Italy, 24-28 March, 2003, Univ. of Padua (2003), p. 77.
[390] Shamolin, MV, New integrable cases and families of portraits in the plane and spatial dynamics of a rigid body interacting with a medium, J. Math. Sci., 114, 919-975, (2003) · Zbl 1067.70006
[391] Shamolin, MV, Classes of variable dissipation systems with nonzero Mean in the dynamics of a rigid body, J. Math. Sci., 122, 2841-2915, (2004) · Zbl 1140.70456
[392] M. V. Shamolin, “Some cases of integrability in dynamics of a rigid body interacting with a resisting medium,” in: Abstracts of Reports of International Conference on Differential Equations and Dynamical Systems, Suzdal’, July 5-10, 2004 [in Russian], Vladimir State University, Vladimir (2004), pp. 296-298.
[393] M. V. Shamolin, “Mathematical model of interaction of a rigid body with a resisting medium in a jet flow,” in: Abs. Part 1, 76 Annual Sci. Conf. (GAMM), Luxembourg, March 28 - April 1, 2005, Univ. du Luxembourg (2005), pp. 94-95.
[394] M. V. Shamolin, “Some cases of integrability in 3D dynamics of a rigid body interacting with a medium,“ in: Book of Abst. IMA Int. Conf. “Recent Advances in Nonlinear Mechanics,” Aberdeen, Scotland, August 30-September 1, 2005, IMA, Aberdeen (2005), p. 112. · Zbl 0451.22008
[395] M. V. Shamolin, “Structural stable vector fields in rigid body dynamics,” in: Abst. of 8th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2005), Lodz, Poland, Dec. 12-15, 2005, Tech. Univ. Lodz (2005), p. 78.
[396] M. V. Shamolin, “Structural stable vector fields in rigid body dynamics,” in: Proc. of 8th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2005), Lodz, Poland, Dec. 12-15, 2005, Tech. Univ. Lodz (2005), Vol. 1, pp. 429-436.
[397] M. V. Shamolin, “Almost conservative systems in dynamics of a rigid body,” in: Book of Abs., 77th Annual Meeting of GAMM, March 27th-31st, 2006, Technische Univ. Berlin, Technische Univ. Berlin (2006), p. 74.
[398] M. V. Shamolin, “On the problem of a symmetric body motion in a resisting medium,” in: Book of Abst. of EMAC-2007 (1-4 July, 2007, Hobart, Australia), Univ. Tasmania, Hobart, Australia (2007), p. 25.
[399] M. V. Shamolin, “The cases of complete integrability in dynamics of a rigid body interacting with a medium,” in: Book of Abs. of Int. Conf. on the Occasion of the 150th Birthday of A. M. Lyapunov (June 24-30, 2007, Kharkiv, Ukraine), Kharkiv, Verkin Inst. Low Temper. Physics Engineer, NASU (2007), pp. 147-148.
[400] M. V. Shamolin, “The cases of integrability in terms of transcendental functions in dynamics of a rigid body interacting with a medium,” in: Abst. of 9th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2007), Lodz, Poland, Dec. 17-20, 2007, Tech. Univ. Lodz (2007), p. 115.
[401] M. V. Shamolin, “The cases of integrability in terms of transcendental functions in dynamics of a rigid body interacting with a medium,” in: Proc. of 9th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2007), Lodz, Poland, Dec. 17-20, 2007 Tech. Univ. Lodz (2007), Vol. 1, pp. 415-422.
[402] M. V. Shamolin, “The cases of integrability in 2D-, 3D- and 4D-rigid body,“ in: Abstr. of Short Commun. and Post. of Int. Conf., “Dynamical Methods and Mathematical Modelling,” Valladolid, Spain (Sept. 18-22, 2007), ETSII, Valladolid (2007), p. 31.
[403] M. V. Shamolin, “4D rigid body and some cases of integrability,” in: Abstracts of ICIAM07, Zurich, Switzerland, June 16-20, 2007, ETH Zurich (2007), p. 311.
[404] M. V. Shamolin, “Methods of analysis of dynamical systems with various dissipation in dynamics of a rigid body,” in: ENOC-2008, CD-Proc., June 30-July 4, 2008 [in Russian], St.-Petersburg, Russia, 6 p. · Zbl 1393.37096
[405] M. V. Shamolin, “Methods of analysis of dynamical systems with various dissipation in dynamics of a rigid body,” in: ENOC-2008, Final Program and Abstracts, June 30-July 4, 2008, St.-Petersburg, Russia [in Russian], SPSU, St.-Petersburg (2008), p. 78. · Zbl 1393.37096
[406] Shamolin, MV, Some methods of analysis of the dynamical systems with various dissipation in dynamics of a rigid body, Proc. Appl. Math. Mech., 8, 10137-10138, (2008) · Zbl 1393.37096
[407] M. V. Shamolin, “Dynamical systems with variable dissipation: Methods and applications,” in: Proc. of 10th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2009), Lodz, Poland, Dec. 7-10, 2009, Tech. Univ. Lodz (2009), pp. 91-104. · Zbl 1189.37022
[408] M. V. Shamolin, “Dynamical systems with variable dissipation: Methods, and applications,” in: Programme/Abstract/Participants of XVI International Congress on Mathematical Physics (ICMP09), Prague, Czech Rep., August 3-8, 2009, Prague (2009), p. 33. · Zbl 1189.37022
[409] Shamolin, MV, New cases of integrability in dynamics of a rigid body with the cone form of its shape interacting with a medium, Proc. Appl. Math. Mech., 9, 139-140, (2009)
[410] M. V. Shamolin, “The various cases of complete integrability in dynamics of a rigid body interacting with a medium,” in: Multibody Dynamics, ECCOMAS Thematic Conf. Warsaw, Poland, 29 June-2 July 2009, Book of Abst., Polish Acad. Sci., Warsaw (2009), pp. 276-277. · Zbl 1067.93020
[411] M. V. Shamolin, “The various cases of complete integrability in dynamics of a rigid body interacting with a medium,” in: Multibody Dynamics, Abstracts of Reports of ECCOMAS Thematic Conf. Warsaw, Poland, 29 June-2 July 2009, CD-Proc., Polish Acad. Sci., Warsaw (2009), 20 p.
[412] M. V. Shamolin, “Dynamical systems with various dissipation: Background, methods, applications,“ Book of Abs. of XXXVIII Summer School-Conf. “Advances Problems in Mechanics” (APM 2010), July 1-5, 2010, St.-Petersburg (Repino), Russia [in Russian], St.-Petersburg, IPME (2010), pp. 86-87.
[413] M. V. Shamolin, Dynamical systems with various dissipation: Background, methods, applications,“ in: CD-Proc. of XXXVIII Summer School-Conf. “Advances Problems in Mechanics” (APM 2010), July 1-5, 2010, St.-Petersburg (Repino), Russia [in Russian], St.-Petersburg, IPME (2010), pp. 612-621.
[414] Shamolin, MV, Integrability and nonintegrability in terms of transcendental functions in dynamics of a rigid body, Proc. Appl. Math. Mech., 10, 63-64, (2010)
[415] M. V. Shamolin, “Cases of complete integrability in transcendental functions in dynamics and certain invariant indices,” in: CD-Proc. 5th Int. Sci. Conf. on Physics and Control PHYSCON 2011, Leon, Spain, September 5-8, 2011, Leon, Spain, 5 p.
[416] M. V. Shamolin, “Cases of complete integrability in transcendental functions in dynamics and certain invariant indices,” in: 5th Int. Sci. Conf. on Physics and Control PHYSCON 2011, Leon, Spain, September 5-8, 2011, Leon, Spain, p. 135.
[417] M. V. Shamolin, “Variety of the cases of integrability in dynamics of a 2D-, 3D-, and 4D-rigid body interacting with a medium,” in: Proc. of 11th Conf. on Dynamical Systems (Theory and Applications) (DSTA 2011), Lodz, Poland, Dec. 5-8, 2011, Tech. Univ. Lodz (2011), pp. 11-24.
[418] M. V. Shamolin, “Cases of complete integrability in transcendental functions in dynamics and certain invariant indices,” in: 83rd Annual Scientific Conference of the International Association of Applied Mathematics and Mechanics. Book of Abstracts, Darmstadt, Germany, March 26-30, 2012, TU Darmstadt, Darmstadt (2012), p. 48.
[419] M. V. Shamolin, “Cases of integrability in dynamics of a rigid body interacting with a resistant medium,” in: Abstract Book, 23th International Congress of Theoretical and Applied Mechanics, August 19-24, 2012, Beijing, China, China Science Literature Publishing House, Beijing (2012), p. 51. · Zbl 1277.37104
[420] M. V. Shamolin, “Cases of integrability in dynamics of a rigid body interacting with a resistant medium,” in: CD-Proc., 23th International Congress of Theoretitical and Applied Mechanics, August 19-24, 2012, Beijing, China, China Science Literature Publishing House, Beijing (2012), 2 p. · Zbl 1277.37104
[421] M. V. Shamolin, “Variety of the cases of integrability in dynamics of a 2D-, and 3D-rigid body interacting with a medium,” in: 8th ESMC 2012, CD-Materials (Graz, Austria, July 9-13, 2012), Graz, Graz, Austria (2012), 2 p.
[422] Shorygin, OP; Shul’man, NA, Reflection of a disk in water with angle of attack, Uchenye Zapiski TsAGI, 8, 12-21, (1977)
[423] J. L. Singh, Classical Dynamics [Russian translation], Fizmatgiz, Moscow (1963).
[424] S. Smale, “Rough systems are not dense,” in: A Collection of Translations, Mathematics [in Russian], 11, No. 4, 107-112 (1967).
[425] Smale, S, Differentiable dynamical systems, Usp. Mat. Nauk, 25, 113-185, (1970) · Zbl 0205.54201
[426] V. A. Steklov, On Rigid Body Motion in a Fluid [in Russian], Khar’kov (1893).
[427] V. V. Stepanov, A Course of Differential Equations [in Russian], Fizmatgiz, Moscow (1959).
[428] Strekalov, VV, Reflection in entrance of a disk in water whose plane is close to vertical plane, Uchenye Zapiski TsAGI, 8, 66-73, (1977)
[429] E. I. Suvorova and M. V. Shamolin, “Poincaré topographical systems and comparison systems of higher orders,“ in: Mathematical Conference “Contemporary Methods of Function Theory and Related Problems,” Voronezh, January 26-February 2, 2003 [in Russian], Voronezh State University, Voronezh (2003), pp. 251-252.
[430] G. K. Suslov, Theoretical Mechanics [in Russian], Gostekhizdat, Moscow (1946).
[431] V. V. Sychev, A. I. Ruban, and G. L. Korolev, Asymptotic Theory of Separation Flows [In Russian], Nauka, Moscow (1987). · Zbl 0944.76003
[432] V. G. Tabachnikov, “Stationary characteristics of wings at small velocities under whole range of angles of attack,” in: Proceedings of Central Aero-Hydrodynamical Institute [in Russian], Issue 1621, Moscow (1974), pp. 18-24.
[433] Trofimov, VV, Embeddings of finite groups in compact Lie groups by regular elements, Dokl. Akad. Nauk SSSR, 226, 785-786, (1976)
[434] Trofimov, VV, Euler equations on finite-dimensional solvable Lie groups, Izv. Akad. nauk SSSR, Ser. Mat., 44, 1191-1199, (1980) · Zbl 0451.22008
[435] Trofimov, VV, Symplectic structures on automorphism groups of symmetric spaces, Vestn. MGU, Ser. 1, Mat., Mekh., 6, 31-33, (1984)
[436] Trofimov, VV; Fomenko, AT, A methodology for constructing Hamiltonian flows on symmetric spaces and integrability of certain hydrodynamical systems, Dokl. Akad. Nauk SSSR, 254, 1349-1353, (1980)
[437] V. V. Trofimov and M. V. Shamolin, “Dissipative systems with nontrivial generalized Arnol’d-Maslov classes,” in: Abstracts of Reports of P. K. Rashevskii Workshop in Vector and Tensor Analysis [in Russian], Vestn. MGU, Ser. 1, Mat., Mekh., 2, 62 (2000). · Zbl 1212.70011
[438] Trofimov, VV; Shamolin, MV, Geometrical and dynamical invariants of integrable Hamiltonian and dissipative systems, Fund. Prikl. Mat., 16, 3-229, (2010)
[439] S. V. Vishik and S. F. Dolzhanskii, “Analogs of Euler-Poisson equations and magnetic electrodynamical related to Lie groups,” Dokl. Akad. Nauk SSSR, 238, No. 5, 1032-1035.
[440] Yu. G. Vyshkvarko and M. V. Shamolin, “Some problems of qualitative theory in rigid body dynamics”, in: All-Russian Conference in Honour of 110th Anniversary of Mathematics Faculty of MPSU ‘Mathematics, Informatics and Methodology of Its Teaching. Moscow, March 14-16’ [in Russian], Moscow, MPSU, pp. 40-41 (2011).
[441] Weyher, Observations sur le Vol Plane par Obres, “L’Aeronaute,” (1890).
[442] E. T. Whittecker, Analytical Dynamics [Russian translation], ONTI, Moscow (1937).
[443] N. E. Zhukovskii, “On a fall of light oblong bodies rotating around their longitudinal axis,” in: A Complete Collection of Works [in Russian], Vol. 5, Fizmatgiz, Moscow (1937), pp. 72-80, 100-115.
[444] N. E. Zhukovski, “On bird soaring,” in: A Complete Collection of Works [in Russian] Vol. 5, Fizmatgiz, Moscow (1937), pp. 49-59.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.