Low-dimensional and multidimensional pendulums in nonconservative fields. I. (English. Russian original) Zbl 1423.70019

Shamolin, M. V.

J. Math. Sci., New York 233, No. 2, 173-299 (2018); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 134 (2017).

Summary: In this review, we discuss new cases of integrable systems on the tangent bundles of finitedimensional spheres. Such systems appear in the dynamics of multidimensional rigid bodies in nonconservative fields. These problems are described by systems with variable dissipation with zero mean. We found several new cases of integrability of equations of motion in terms of transcendental functions (in the sense of the classification of singularities) that can be expressed as finite combinations of elementary functions.

MSC:

70E17	Motion of a rigid body with a fixed point
70-02	Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems
37E10	Dynamical systems involving maps of the circle
37N05	Dynamical systems in classical and celestial mechanics

Keywords:

fixed rigid body; pendulum; multidimensional body; integrable system; variable dissipation system; transcendental first integral

References:

[1]	Aidagulov, RR; Shamolin, MV, A certain improvement of Conway algorithm, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 3, 53-55, (2005) · Zbl 1104.03037
[2]	Aidagulov, RR; Shamolin, MV, Phenomenological approach to definition of interphase forces, Dokl. Ross. Akad. Nauk, 412, 44-47, (2007)
[3]	Aidagulov, RR; Shamolin, MV, Archimedean uniform structure, Sovr. Mat. Fundam. Napr., 23, 46-51, (2007)
[4]	Aidagulov, RR; Shamolin, MV, General spectral approach to continuous medium dynamics, Sovr. Mat. Fundam. Napr., 23, 52-70, (2007)
[5]	Aidagulov, RR; Shamolin, MV, Varieties of continuous structures, Sovr. Mat. Fundam. Napr., 23, 71-86, (2007)
[6]	R. R. Aidagulov and M. V. Shamolin, “Groups of colors,” in: Sovr. Mat. Prilozh., 62, 15-27 (2009). · Zbl 1214.16029
[7]	Aidagulov, RR; Shamolin, MV, Pseudodifferential operators in the theory of multiphase, multi-rate flows, Sovr. Mat. Prilozh., 65, 11-30, (2009) · Zbl 1288.35493
[8]	Aidagulov, RR; Shamolin, MV, Averaging operators and real equations of hydromechanics, Sovr. Mat. Prilozh., 65, 31-47, (2009) · Zbl 1288.76004
[9]	Aidagulov, RR; Shamolin, MV, Integration formulas of tenth order and higher, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 4, 3-7, (2010) · Zbl 1304.65112
[10]	Andreev, AV; Shamolin, MV, Mathematical modeling of a medium interaction onto rigid body and new two-parametric family of phase portraits, Vestn. Samar. Univ. Estestv. Nauki, No., 10, 109-115, (2014) · Zbl 1353.70011
[11]	A. A. Andronov, Collection of Works [in Russian], Izd. Akad. Nauk SSSR, Moscow (1956).
[12]	Andronov, AA; Pontryagin, LS, Rough systems, Dokl. Akad. Nauk SSSR, 14, 247-250, (1937) · Zbl 0016.11301
[13]	A. A. Andronov, A. A. Vitt, and S. E. Khaikin, Oscillation Theory [in Russian], Nauka, Moscow (1981). · Zbl 0188.56304
[14]	D. V. Anosov, “Geodesic flows on closed Riemannian manifolds of negative curvature,” Tr. Mat. Inst. Akad. Nauk SSSR, 90 (1967). · Zbl 0163.43604
[15]	P. Appel, Theoretical Mechanics [Russian translation],Vols. I, II, Fizmatgiz, Moscow (1960).
[16]	Arnold, VI, Hamiltonian property of Euler equations of rigid body dynamics in an ideal fluid, Usp. Mat. Nauk, 24, 225-226, (1969) · Zbl 0181.54204
[17]	V. I. Arnold, Mathematical Methods of Classical Mechanics [in Russian], Nauka, Moscow (1989). · Zbl 0692.70003 · doi:10.1007/978-1-4757-2063-1
[18]	V. I. Arnold, 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 (VINITI), Moscow (1985). · Zbl 1105.70002
[19]	N. N. Bautin and E. A. Leontovich, Methods and Tools for Qualitative Study of Dynamical Systems on the Plane [in Russian], Nauka, Moscow (1976).
[20]	V. V. Beletskii, Artificial Satellite Motion with Respect to Center of Mass [in Russian], Nauka, Moscow (1965). · Zbl 0138.20301
[21]	Belyaev, AV, On many-dimensional body motion with clumped point in gravity force field, Mat. Sb., 114, 465-470, (1981)
[22]	I. Bendixon, “On curves defined by differential equations,” Usp. Mat. Nauk, 9 (1941).
[23]	M. Berger, Geometry [Russian translation], Vols. I, II, Mir, Moscow (1984). · Zbl 0598.51017
[24]	A. L. Besse, Manifolds with Closed Geodesics [Russian translation], Mir, Moscow (1981).
[25]	Bivin, YK; Viktorov, VV; Stepanov, LL, Study of rigid body motion in a clayey medium, Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, 2, 159-165, (1978)
[26]	Bivin, YK; Glukhov, YM; Permyakov, YV, Vertical entrance of rigid bodies into water, Izv. Akad. Nauk SSSR. Mekh. Zhidkosti Gaza, 6, 3-9, (1985)
[27]	G. D. Birkhoff, Dynamical Systems [Russian translation], Gostekhizdat, Moscow-Leningrad (1941).
[28]	R. L. Bishop, Oscillations [Russian translation], Nauka, Moscow (1986).
[29]	G. A. Bliss, Lectures on the Calculus of Variations [Russian translation], Gostekhizdat, Moscow (1941).
[30]	O. I. Bogoyavlenskii, Methods of Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics [in Russian], Nauka, Moscow (1980). · Zbl 0506.76078
[31]	Bogoyavlenskii, OI, Some integrable cases of Euler equation, Dokl. Akad. Nauk SSSR, 287, 1105-1108, (1986)
[32]	Bogoyavlenskii, OI; Ivakh, GF, Topological analysis of integrable cases of V. A. Steklov, Usp. Mat. Nauk, 40, 145-146, (1985) · Zbl 0604.76010
[33]	Boiko, GL; Eroshin, VA, Finding overloadings under a shock profile on fluid surface, Izv. Akad. Nauk SSSR. Mekh. Zhidkosti Gaza, 1, 35-38, (1975)
[34]	Borisenok, IT; Shamolin, MV, Solution of differential diagnosis problem, Fundam. Prikl. Mat., 5, 775-790, (1999) · Zbl 0967.93033
[35]	Borisenok, IT; Shamolin, MV, Solution of differential diagnosis problem by statistical trial method, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 1, 29-31, (2001)
[36]	Brailov, AV, Some cases of complete integrability of Euler equations and applications, Dokl. Akad. Nauk SSSR, 268, 1043-1046, (1983) · Zbl 0544.58011
[37]	A. D. Bryuno, Local Method of Nonlinear Analysis of Differential Equations [in Russian], Nauka, Moscow (1979). · Zbl 0496.34002
[38]	N. Bourbaki, Integration [Russian translation], Nauka, Moscow (1970). · Zbl 0213.07501
[39]	N. Bourbaki, Lie Groups and Algebras [Russian translation], Mir, Moscow (1972). · Zbl 0249.22001
[40]	Burov, AA; Subkhankulov, GI, On rigid body motion in magnetic field, Prikl. Mat. Mekh., 50, 960-966, (1986) · Zbl 0631.70002
[41]	G. S. Byushgens and R. V. Studnev, Dynamics of Longitudinal and Lateral Motion [in Russian], Mashinostroenie, Moscow (1969).
[42]	G. S. Byushgens and R. V. Studnev, Airplane Dynamics. Spatial Motion [in Russian], Mashinostroenie, Moscow (1988).
[43]	Byalyi, ML, On first integrals polynomial in impulses for a mechanical system on a twodimensional torus, Funkts. Anal. Prilozh., 21, 64-65, (1987) · Zbl 0668.58014
[44]	Ch. J. de la Vallée Poussin, Lectures on Theoretical Mechanics [Russian translation], Vols. I, II, IL, Moscow (1948, 1949).
[45]	S. V. Vishik and S. F. Dolzhanskii, “Analogs of Euler-Poisson equations and magnetoelectrodynamics related to Lie groups,” Dokl. Akad. Nauk SSSR, 238, No. 5, 1032-1035.
[46]	F. R. Gantmakher, Lectures on Analytical Mechanics [in Russian], Nauka, Moscow (1960). · Zbl 0212.56701
[47]	Georgievskii, DV; Shamolin, MV, Kinematics and mass geometry of a rigid body with a fixed point in ℝ\^{}{\(n\)}, Dokl. Ross. Akad. Nauk, 380, 47-50, (2001)
[48]	Georgievskii, DV; Shamolin, MV, Generalized dynamical Euler equations for a rigid body with a fixed point in ℝ\^{}{\(n\)}, Dokl. Ross. Akad. Nauk, 383, 635-637, (2002)
[49]	Georgievskii, DV; Shamolin, MV, First integrals of equations of motion for a generalized gyroscope in ℝ\^{}{\(n\)}, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 5, 37-41, (2003)
[50]	Georgievskii, DV; Shamolin, MV, 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, Sovr. Mat. Prilozh., 65, 3-10, (2009) · Zbl 1180.00019
[51]	Georgievskii, DV; Shamolin, MV, 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, Sovr. Mat. Prilozh., 76, 3-10, (2012) · Zbl 1260.00024
[52]	Georgievskii, DV; Shamolin, MV, Levi-Civita symbols, generalized vector products, and new integrable cases in mechanics of multidimensional bodies, Sovr. Mat. Prilozh., 76, 22-39, (2012) · Zbl 1278.70007
[53]	E. B. Gledzer, F. S. Dolzhanskii, and A. M. Obukhov, Systems of Hydrodynamic Type and Their Applications [in Russian], Nauka, Moscow (1981). · Zbl 0512.76003
[54]	C. Godbillon, Differential Geometry and Analytical Mechanics [Russian translation], Mir, Moscow (1973).
[55]	V. V. Golubev, Lectures on Analytical Theory of Differential Equations [in Russian], Gostekhizdat, Moscow (1950). · Zbl 0038.24201
[56]	V. V. Golubev, Lectures on Integrating Equations of Heavy Body Motion around a Fixed Point [in Russian], Gostekhizdat, Moscow-Leningrad (1953). · Zbl 0051.15103
[57]	P. Griffits, Exterior Differential Systems and the Calculus of Variations [Russian translation], Mir, Moscow (1986).
[58]	Grobman, DM, Topological classification of neighborhoods of a singular point in \(n\)-dimensional space, Mat. Sb., 56, 77-94, (1962) · Zbl 0142.34402
[59]	M. I. Gurevich, Jet Theory of Ideal Fluid [in Russian], Nauka, Moscow (1979).
[60]	Dubrovin, BA; Novikov, SP, On Poisson brackets of hydrodynamic type, Dokl. Akad. Nauk SSSR, 279, 294-297, (1984) · Zbl 0591.58012
[61]	B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry. Theory and Applications [in Russian], Nauka, Moscow (1979).
[62]	Eroshin, VA, Plate reflection from ideal incompressible fluid surface, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 6, 99-104, (1970) · Zbl 0207.25603
[63]	Eroshin, VA, Submergence of a disk in a compressible fluid at an angle to a free surface, Izv. Akad. Nauk SSSR, Mekh. Zhidkosti Gaza, 2, 142-144, (1983)
[64]	Eroshin, VA; Samsonov, VA; Shamolin, MV, Model problem of body drag in a resisting medium under streamline flow-around, Izv. Ross. Akad. Nauk. Mekh. Zhidkosti Gaza, 3, 23-27, (1995)
[65]	Eroshin, VA; Konstantinov, GA; Romanenkov, NI; Yakimov, YL, Experimental finding of pressure on a disk under its submergence in a compressible fluid at an angle to a free surface, Izv. Akad. Nauk SSSR. Mekh. Zhidkosti Gaza, 2, 21-25, (1988)
[66]	Eroshin, VA; Romanenkov, NI; Serebryakov, IV; Yakimov, YL, Hydrodynamic forces under a shock of blunt bodies on compressible fluid surface, Izv. Akad. Nauk SSSR. Mekh. Zhidkosti Gaza, 6, 44-51, (1980)
[67]	N. E. Zhukovskii, “On a fall of light oblong bodies rotating around their longitudinal axis,” in: Complete Collection of Works [in Russian], Vol. 5, Fizmatgiz, Moscow (1937), pp. 72-80, 100-115.
[68]	N. E. Zhukovskii, “On bird soaring,” in: Complete Collection of Works [in Russian], Vol. 5, Fizmatgiz, Moscow (1937), pp. 49-59.
[69]	H. Seifert and W. Threifall, Topology [Russian translation], Gostekhizdat, Moscow-Leningrad (1938).
[70]	Ivanova, TA, On Euler equations in models of theoretical physics, Mat. Zametki, 52, 43-51, (1992)
[71]	A. Yu. Ishlinsky, Orientation, Gyroscopes, and Inertial Navigation [in Russian], Nauka, Moscow (1976).
[72]	V. V. Kozlov, Qualitative Analysis Methods in Rigid Body Dynamics [in Russian], Izd. Mosk. Univ., Moscow (1980). · Zbl 0557.70009
[73]	Kozlov, VV, Integrability and nonintegrability in Hamiltonian mechanics, Usp. Mat. Nauk, 38, 3-67, (1983) · Zbl 0525.70023
[74]	Kozlov, VV, On rigid body fall in ideal fluid, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 5, 10-17, (1989)
[75]	Kozlov, VV, To problem of heavy rigid body fall in a resisting medium, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 1, 79-87, (1990)
[76]	G. Lamb, Hydrodynamics [Russian translation], Fizmatgiz, Moscow (1947).
[77]	S. Lefschetz, Geometric Theory of Differential Equations [Russian translation], IL, Moscow (1961). · Zbl 0094.05803
[78]	J. U. Leech, Classical Mechanics [Russian translation], IL, Moscow (1961).
[79]	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], Izd. Mosk. Univ., Moscow (1986).
[80]	Lunev, VV, A hydrodynamical analogy of problem of rigid body motion with a fixed point in Lorenz force field, Dokl. Akad. Nauk SSSR, 276, 351-355, (1984)
[81]	A. M. Lyapunov, “A new integrability case of equations of rigid body motion in a fluid,” in: Collection of Works [in Russian], Vol. I, Izd. Akad. Nauk SSSR, Moscow (1954), pp. 320-324.
[82]	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.
[83]	W. Miller, Symmetry and Separation of Variables [Russian translation], Mir, Moscow (1981). · Zbl 0531.35001
[84]	V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations [in Russian], Gostekhizdat, Moscow-Leningrad (1949).
[85]	Z. Nitetski, Introduction to Differential Dynamics [Russian translation], Mir, Moscow (1975).
[86]	V. A. Odareev, Decompositional Analysis of Dynamics and Stability of Longitudinal Perturbed Motion of the Ekranoplan [in Russian], Doctoral Dissertation, MGAI, Moscow (1995).
[87]	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], Izd. Mosk. Univ., Moscow (1998), pp. 28-46.
[88]	Yu. M. Okunev, V. A. Samsonov, B. Ya. Lokshin, M. Z. Dosaev, L. A. Klimina, Yu. D. Selyutskii, O. G. Privalova, M. V. Shamolin, and A. I. Kobrin, “Problems of control of motion of the bodies in a continuous medium,” in: Scientific Report of Institute of Mechanics, Moscow State University [in Russian], No. 5103, Institute of Mechanics, Moscow State University, Moscow (2010).
[89]	Okunev, YM; Shamolin, MV, On integrability in elementary functions of certain classes of complex nonautonomous equations, Sovr. Mat. Prilozh., 65, 122-131, (2009)
[90]	J. Palis and W. De Melu, Geometric Theory of Dynamical Systems. An Introduction [Russian translation], Mir, Moscow (1986).
[91]	Perelomov, AM, Several remarks on integration of equations of rigid body motion in ideal fluid, Funkts. Anal. Prilozh., 15, 83-85, (1981) · Zbl 0476.22014 · doi:10.1007/BF01082279
[92]	Polyakov, NL; Shamolin, MV, On closed symmetric functional classes preserving any single predicate, Vestn. Sam. Univ. Estestv. Nauki, 6, 61-73, (2013)
[93]	Polyakov, NL; Shamolin, MV, On a generalization of arrows impossibility theorem, Dokl. Ross. Akad. Nauk, 456, 143-145, (2014)
[94]	Pokhodnya, NV; Shamolin, MV, New integrable case in dynamics of a multidimensional body, Vestn. Sam. Univ. Estestv. Nauki, 9, 136-150, (2012) · Zbl 1327.70009
[95]	N. V. Pokhodnya and M. V. Shamolin, “Certain conditions of integrability of dynamical systems in transcendental functions,” Vestn. Sam. Univ. Estestv. Nauki, No. 9/1 (110), 35-41 (2013). · Zbl 1328.34004
[96]	Pokhodnya, NV; Shamolin, MV, Integrable systems on the tangent bundle of a multidimensional sphere, Vestn. Sam. Univ. Estestv. Nauki, No., 7, 60-69, (2014) · Zbl 1353.70017
[97]	H. Poincaré, On Curves Defined by Differential Equations [Russian translation], OGIZ, Moscow-Leningrad (1947).
[98]	H. Poincaré, “New methods in celestial mechanics,” in: Selected Works [Russian translation], Vols. 1, 2, Nauka, Moscow (1971, 1972). · Zbl 0232.01018
[99]	H. Poincaré, On Science [Russian translation], Nauka, Moscow (1983). · Zbl 0536.01036
[100]	V. A. Samsonov, Issues on Mechanics. Some Problems, Phenomena, and Paradoxes [in Russian], Nauka, Moscow (1980).
[101]	Samsonov, VA; Shamolin, MV, Problem on body motion in a resisting medium, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 3, 51-54, (1989) · Zbl 0705.70008
[102]	Samsonov, VA; Shamolin, MV, A model problem of body motion in a medium with streamline flow-around, No. 3969, (1990), Moscow
[103]	V. A. Samsonov and M. V. Shamolin, “Problem of body drag in a medium under streamline flow-around,” in: Scientific Report of Institute of Mechanics, Moscow State Univ. [in Russian], No. 4141, Institute of Mechanics, Moscow State Univ., Moscow (1991).
[104]	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-around,” in: Scientific Report of Institute of Mechanics, Moscow State Univ. [in Russian], No. 4396, Institute of Mechanics, Moscow State Univ., Moscow (1995).
[105]	L. I. Sedov, Mechanics of Continuous Media [in Russian], Vols. 1, 2, Nauka, Moscow (1983, 1984).
[106]	Selivanova, NY; Shamolin, MV, Local solvability of a certain problem with free boundary, Vestn. Sam. Univ. Estestv. Nauki, No., 8, 86-94, (2011)
[107]	Selivanova, NY; Shamolin, MV, Local solvability of a one-phase problem with free boundary, Sovr. Mat. Prilozh., 78, 99-108, (2012)
[108]	Selivanova, NY; Shamolin, MV, Studying the interphase zone in a certain singular-limit problem, Sovr. Mat. Prilozh., 78, 109-118, (2012) · Zbl 1321.35172
[109]	Selivanova, NY; Shamolin, MV, Local solvability of the capillar problem, Sovr. Mat. Prilozh., 78, 119-125, (2012)
[110]	Selivanova, NY; Shamolin, MV, Quasi-stationary Stefan problem with values on front depending on its geometry, Sovr. Mat. Prilozh., 78, 126-134, (2012)
[111]	J. L. Singh, Classical Dynamics [Russian translation], Fizmatgiz, Moscow (1963). · Zbl 0118.39901
[112]	Smale, S, Differentiable dynamical systems, Usp. Mat. Nauk, 25, 113-185, (1970) · Zbl 0205.54201
[113]	V. A. Steklov, On Rigid Body Motion in a Fluid [in Russian], Kharkov (1893).
[114]	G. K. Suslov, Theoretical Mechanics [in Russian], Gostekhizdat, Moscow (1946).
[115]	V. V. Sychev, A. I. Ruban, Vik. V. Sychev, and G. L. Korolev, Asymptotic Theory of Separation Flows [in Russian], Nauka, Moscow (1987). · Zbl 1139.76003
[116]	V. G. Tabachnikov, “Stationary characteristics of wings in small velocities under whole range of attack angles,” in: Proc. Central Aero-Hydrodynamical Institute [in Russian], No. 1621, Moscow (1974), pp. 18-24.
[117]	Trofimov, VV, Embeddings of finite groups in compact Lie groups by regular elements, Dokl. Akad. Nauk SSSR, 226, 785-786, (1976)
[118]	Trofimov, VV, Euler equations on finite-dimensional solvable Lie groups, Izv. Akad. Nauk SSSR, Ser. Mat., 44, 1191-1199, (1980) · Zbl 0451.22008
[119]	Trofimov, VV; Shamolin, MV, Geometrical and dynamical invariants of integrable Hamiltonian and dissipative systems, Fundam. Prikl. Mat., 16, 3-229, (2010)
[120]	E. T. Whittecker, Analytical Dynamics [Russian translation], ONTI, Moscow (1937).
[121]	P. Hartman, Ordinary Differential Equations [Russian translation], Mir, Moscow (1970). · Zbl 0214.09101
[122]	S. A. Chaplygin, “On motion of heavy bodies in an incompressible fluid,” in: Complete Collection of Works [in Russian], Vol. 1, Izd. Akad. Nauk SSSR, Leningrad (1933), pp. 133-135.
[123]	S. A. Chaplygin, Selected Works [in Russian], Nauka, Moscow (1976).
[124]	M. V. Shamolin, Qualitative Analysis of a Model Problem of Body Motion in a Medium with Streamline Flow-Around [in Russian], Candidate Dissertation, Moscow Univ., Moscow (1991).
[125]	Shamolin, MV, Closed trajectories of different topological types in problem of body motion in a medium with resistance, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 2, 52-56, (1992)
[126]	Shamolin, MV, Problem of body motion in a medium with resistance, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 1, 52-58, (1992) · Zbl 0753.70007
[127]	Shamolin, MV, Classification of phase portraits in problem of body motion in a resisting medium in the presence of a linear damping moment, Prikl. Mat. Mekh., 57, 40-49, (1993) · Zbl 0820.76018
[128]	Shamolin, MV, Applications of Poincaré topographical system methods and comparison systems in some concrete systems of differential equations, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 2, 66-70, (1993)
[129]	Shamolin, MV, Existence and uniqueness of trajectories having infinitely distant points as limit sets for dynamical systems on a plane, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 1, 68-71, (1993) · Zbl 0815.34002
[130]	Shamolin, MV, A new two-parameter family of phase portraits in problem of a body motion in a medium, Dokl. Ross. Akad. Nauk, 337, 611-614, (1994)
[131]	M. V. Shamolin, “Relative structural stability of dynamical systems for problem of body motion in a medium,” in: Analytical, Numerical, and Experimental Methods in Mechanics. A Collection of Scientific Works [in Russian], Izd. Mosk. Univ., Moscow (1995), pp. 14-19.
[132]	Shamolin, MV, Definition of relative roughness and two-parameter family of phase portraits in rigid body dynamics, Usp. Mat. Nauk, 51, 175-176, (1996) · Zbl 0874.70006 · doi:10.4213/rm940
[133]	Shamolin, MV, Periodic and Poisson stable trajectories in problem of body motion in a resisting medium, Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 2, 55-63, (1996)
[134]	Shamolin, MV, Variety of types of phase portraits in dynamics of a rigid body interacting with a resisting medium, Dokl. Ross. Akad. Nauk, 349, 193-197, (1996)
[135]	Shamolin, MV, Introduction to problem of body drag in a resisting medium and a new twoparameter family of phase portraits, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 4, 57-69, (1996) · Zbl 0923.70008
[136]	Shamolin, MV, On an integrable case in spatial dynamics of a rigid body interacting with a medium, Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 2, 65-68, (1997)
[137]	Shamolin, MV, Spatial Poincaré topographical systems and comparison systems, Usp. Mat. Nauk, 52, 177-178, (1997) · Zbl 0915.58062 · doi:10.4213/rm859
[138]	Shamolin, MV, On integrability in transcendental functions, Usp. Mat. Nauk, 53, 209-210, (1998) · Zbl 0925.34003 · doi:10.4213/rm53
[139]	M. V. Shamolin, “Methods of nonlinear analysis in dynamics of a rigid body interacting with a medium,“ in: CD Proc. of the Congress “Nonlinear Analysis and Its Applications,” Moscow, Russia, September 1-5, 1998, Moscow (1999), pp. 497-508.
[140]	Shamolin, MV, Families of portraits with limit cycles in plane dynamics of a rigid body interacting with a medium, Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 6, 29-37, (1998)
[141]	Shamolin, MV, Certain classes of partial solutions in dynamics of a rigid body interacting with a medium, Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 2, 178-189, (1999)
[142]	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
[143]	Shamolin, MV, On roughness of dissipative systems and relative roughness and nonroughness of variable dissipation systems, Usp. Mat. Nauk, 54, 181-182, (1999) · Zbl 0968.34039 · doi:10.4213/rm217
[144]	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)
[145]	Shamolin, MV, On limit sets of differential equations near singular points, Usp. Mat. Nauk, 55, 187-188, (2000) · Zbl 0968.34021 · doi:10.4213/rm305
[146]	Shamolin, MV, Jacobi integrability in problem of four-dimensional rigid body motion in a resisting medium, Dokl. Ross. Akad. Nauk, 375, 343-346, (2000)
[147]	Shamolin, MV, On stability of motion of a body twisted around its longitudinal axis in a resisting medium, Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 1, 189-193, (2001)
[148]	Shamolin, MV, Integrability cases of equations for spatial dynamics of a rigid body, Prikl. Mekh., 37, 74-82, (2001) · Zbl 1010.70520
[149]	Shamolin, MV, Complete integrability of equations for motion of a spatial pendulum in a jet flow of medium, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 5, 22-28, (2001) · Zbl 1051.70509
[150]	Shamolin, MV, On integrability of certain classes of nonconservative systems, Usp. Mat. Nauk, 57, 169-170, (2002) · doi:10.4213/rm489
[151]	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
[152]	M. V. Shamolin, Methods for Analysis of Classes of Nonconservative Systems in Dynamics of a Rigid Body Interacting with a Medium [in Russian], Doctoral Dissertation, Moscow Univ., Moscow (2004).
[153]	M. V. Shamolin, Some Problems of Differential and Topological Diagnosis [in Russian], Ekzamen, Moscow (2004).
[154]	Shamolin, MV, A case of complete integrability in spatial dynamics of a rigid body interacting with a medium taking account of rotational derivatives of force moment in angular velocity, Dokl. Ross. Akad. Nauk, 403, 482-485, (2005)
[155]	Shamolin, MV, Comparison of Jacobi integrable cases of plane and spatial body motions in a medium under streamline flow-around, Prikl. Mat. Mekh., 69, 1003-1010, (2005) · Zbl 1100.74546
[156]	Shamolin, MV, On a certain integrable case of equations of dynamics in so(4) \(×\) ℝ\^{}{4}, Usp. Mat. Nauk, 60, 233-234, (2005) · Zbl 1183.70019 · doi:10.4213/rm1688
[157]	M. V. Shamolin, “Model problem of body motion in a resisting medium taking account of dependence of resistance force on angular velocity,” in: Scientific Report of Institute of Mechanics, Moscow State Univ. [in Russian], No. 4818, Institute of Mechanics, Moscow State Univ., Moscow (2006).
[158]	Shamolin, MV, Problem on rigid body spatial drag in a resisting medium, Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 3, 45-57, (2006)
[159]	Shamolin, MV, Complete integrability of equations of motion for a spatial pendulum in medium flow taking account of rotational derivatives of moments of its action force, Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 3, 187-192, (2007)
[160]	Shamolin, MV, A case of complete integrability in dynamics on a tangent bundle of twodimensional sphere, Usp. Mat. Nauk, 62, 169-170, (2007) · Zbl 1137.37325 · doi:10.4213/rm7487
[161]	M. V. Shamolin, Methods of Analysis of Variable Dissipation Dynamical Systems in Rigid Body Dynamics [in Russian], Ekzamen, Moscow (2007). · Zbl 1334.70001
[162]	M. V. Shamolin, Some Problems of Differential and Topological Diagnosis [in Russian], Ekzamen, Moscow (2007).
[163]	Shamolin, MV, Three-parameter family of phase portraits in dynamics of a rigid body interacting with a medium, Dokl. Ross. Akad. Nauk, 418, 46-51, (2008)
[164]	Shamolin, MV, Some model problems of dynamics for a rigid body interacting with a medium, Prikl. Mekh., 43, 49-67, (2007) · Zbl 1164.74395
[165]	Shamolin, MV, New integrable cases in dynamics of a medium-interacting body with allowance for dependence of resistance force moment on angular velocity, Prikl. Mat. Mekh., 72, 273-287, (2008) · Zbl 1189.70045
[166]	Shamolin, MV, Integrability of some classes of dynamic systems in terms of elementary functions, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 3, 43-49, (2008) · Zbl 1212.70011
[167]	M. V. Shamolin, “On integrability in elementary functions of certain classes of nonconservative dynamical systems,” in: Sovr. Mat. Prilozh., 62, 131-171 (2009).
[168]	Shamolin, MV, Dynamical systems with variable dissipation: approaches, methods, and applications, Fundam. Prikl. Mat., 14, 3-237, (2008)
[169]	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) · Zbl 1347.70010
[170]	Shamolin, MV, Generalized problem of differential diagnosis and its possible resolving, Elektron. Model., 31, 97-115, (2009)
[171]	Shamolin, MV, Resolving of diagnosis problem in case of precise trajectory measurements with error, Elektron. Model., 31, 73-90, (2009)
[172]	Shamolin, MV, Diagnosis of failures in certain non-direct control system, Elektron. Model., 31, 55-66, (2009)
[173]	Shamolin, MV, Classification of complete integrability cases in four-dimensional symmetric rigid-body dynamics in a nonconservative field, Sovr. Mat. Prilozh., 65, 132-142, (2009)
[174]	Shamolin, MV, Stability of a rigid body translating in a resisting medium, Prikl. Mekh., 45, 125-140, (2009) · Zbl 1212.70023
[175]	Shamolin, MV, New cases of integrability in the spatial dynamics of a rigid body, Dokl. Ross. Akad. Nauk, 431, 339-343, (2010) · Zbl 1353.70018
[176]	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) · Zbl 1356.70010 · doi:10.4213/rm9320
[177]	Shamolin, MV, Diagnosis of certain system of direct control of aircraft motion, Elektron. Model., 32, 45-52, (2010)
[178]	M. V. Shamolin, “On the problem of the motion of the body with plane front end in a resisting medium,” in: Scientific Report of Institute of Mechanics, Moscow State University [in Russian], No. 5052, Institute of Mechanics, Moscow State University, Moscow (2010).
[179]	Shamolin, MV, Spatial motion of a rigid body in a resisting medium, Prikl. Mekh., 46, 120-133, (2010)
[180]	Shamolin, MV, Motion diagnosis of aircraft in mode of planning lowering, Elektron. Model., 32, 31-44, (2010)
[181]	Shamolin, MV, Comparison of complete integrability cases in dynamics of a two-, three-, and four-dimensional rigid body in a nonconservative field, Sovr. Mat. Prilozh., 76, 84-99, (2012) · Zbl 1277.37104
[182]	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)
[183]	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)
[184]	Shamolin, MV, Diagnosis of hyro-stabilized platform included in control system of aircraft motion, Elektron. Model., 33, 121-126, (2011)
[185]	Shamolin, MV, Dynamical invariants of integrable variable dissipation dynamical systems, Vestn. Nizhegorod. Univ., Part, 2, 356-357, (2011)
[186]	Shamolin, MV, A multiparameter family of phase portraits in the dynamics of a rigid body interacting with a medium, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 3, 24-30, (2011) · Zbl 1433.70008
[187]	Shamolin, MV, Rigid body motion in a resisting medium, Mat. Model., 23, 79-104, (2011) · Zbl 1274.74112
[188]	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)
[189]	Shamolin, MV, New case of complete integrability of the dynamic equations on the tangent stratification of three-dimensional sphere, Vestn. Sam. Univ. Estestv. Nauki, 5, 187-189, (2011)
[190]	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)
[191]	M. V. Shamolin, “Some questions of qualitative theory in dynamics of systems with variable dissipation,” in: Sovr. Mat. Prilozh., 78, 138-147 (2012).
[192]	Shamolin, MV, Complete List of first integrals of dynamic equations of spatial rigid body motion in a resisting medium under assumption of linear damping, Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 4, 44-47, (2012)
[193]	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, Mat. Model., 24, 109-132, (2012) · Zbl 1289.70008
[194]	Shamolin, MV, Complete List of first integrals of dynamic equations of motion of a 4D rigid body in a nonconservative field under the assumption of linear damping, Dokl. Ross. Akad. Nauk, 449, 416-419, (2013)
[195]	Shamolin, MV, A new case of integrability in transcendental functions in the dynamics of solid body interacting with the environment, Avtomat. Telemekh., 8, 173-190, (2013) · Zbl 1297.70003
[196]	Shamolin, MV, New case of integrability in the dynamics of a multidimensional solid in a nonconservative field, Dokl. Ross. Akad. Nauk, 453, 46-49, (2013)
[197]	Shamolin, MV, New case of integrability of dynamic equations on the tangent bundle of a 3-sphere, Usp. Mat. Nauk, 68, 185-186, (2013) · Zbl 1356.70011 · doi:10.4213/rm9541
[198]	Shamolin, MV, On integrability in dynamic problems for a rigid body interacting with a medium, Prikl. Mekh., 49, 44-54, (2013) · Zbl 1284.70010
[199]	M. V. Shamolin, “Variety of integrable cases in dynamics of low- and multi-dimensional rigid bodies in nonconservative force fields,” in: Itogi Nauki i Tekh. Ser. Sovr. Mat. Prilozh. Temat. Obzory [in Russian], 125, All-Russian Institute for Scientific and Technical Information, Russian Academy of Sciences, Moscow (2013), pp. 5-254.
[200]	Shamolin, MV, A new case of integrability in the dynamics of a multidimensional solid in a nonconservative field under the assumption of linear damping, Dokl. Ross. Akad. Nauk, 457, 542-545, (2014)
[201]	M. V. Shamolin, “Variety of integrable cases in spatial dynamics of a rigid body in a nonconservative force fields,” in: Tr. Sem. I. G. Petrovskogo, 30, Moscow State Univ., Moscow (2014), pp. 287-350.
[202]	Shamolin, MV, A multidimensional pendulum in a nonconservative force field, Dokl. Ross. Akad. Nauk, 460, 165-169, (2015)
[203]	Shamolin, MV, Rigid body motion in a resisting medium modelling and analogues with vortex streets, Mat. Model., 27, 33-53, (2015) · Zbl 1340.76015
[204]	Shamolin, MV, Integrable cases in the dynamics of a multi-dimensional rigid body in a nonconservative field in the presence of a tracking force, Fundam. Prikl. Mat., 19, 187-222, (2014)
[205]	Shamolin, MV, Complete List of first integrals of dynamic equations for a multidimensional solid in a nonconservative field, Dokl. Ross. Akad. Nauk, 461, 533-536, (2015)
[206]	Shamolin, MV, New case of complete integrability of dynamics equations on a tangent bundle to the three-dimensional sphere, Vestn. Mosk. Univ. Ser. 1, Mat. Mekh., 3, 11-14, (2015)
[207]	M. V. Shamolin and S. V. Tsyptsyn, “Analytical and numerical study of trajectories of body motion in a resisting medium,” in: Scientific Report of Institute of Mechanics, Moscow State Univ. [in Russian], No. 4289, Institute of Mechanics, Moscow State Univ., Moscow (1993).
[208]	M. V. Shamolin and D. V. Shebarshov, “Some problems of geometry in classical mechanics,” Preprint VINITI No. 1499-V99 (1999).
[209]	M. V. Shamolin and D. V. Shebarshov, “Methods for solving main problem of differential diagnosis,” Preprint VINITI, No. 1500-V99 (1999).
[210]	Shorygin, OP; Shulman, NA, Entry of a disk into water at an attack angle, Uch. Zap. TsAGI, 8, 12-21, (1977)
[211]	D. Arrowsmith and C. Place, Ordinary Differential Equations. Qualitative Theory with Applications [Russian translation], Mir, Moscow (1986). · Zbl 0671.34001
[212]	C. Jacobi, Lectures on Dynamics [Russian translation], ONTI, Moscow (1936).
[213]	Aidagulov, RR; Shamolin, MV, Polynumbers, norms, metrics, and polyingles, J. Math. Sci., 204, 742-759, (2015) · Zbl 1341.53046 · doi:10.1007/s10958-015-2214-y
[214]	Aidagulov, RR; Shamolin, MV, Finsler spaces, bingles, polyingles, and their symmetry groups, J. Math. Sci., 204, 732-741, (2015) · Zbl 1341.53109 · doi:10.1007/s10958-015-2213-z
[215]	Aidagulov, RR; Shamolin, MV, Topology on polynumbers and fractals, J. Math. Sci., 204, 760-771, (2015) · Zbl 1359.37106 · doi:10.1007/s10958-015-2215-x
[216]	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 · doi:10.1007/s10958-008-9190-4
[217]	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 · doi:10.1007/s10958-009-9591-z
[218]	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., 204, 715-731, (2015) · Zbl 1325.00038 · doi:10.1007/s10958-015-2212-0
[219]	Okunev, YM; Shamolin, MV, On the construction of the general solution of a class of complex nonautonomous equations, J. Math. Sci., 204, 787-799, (2015) · Zbl 1354.34029 · doi:10.1007/s10958-015-2218-7
[220]	M. V. Shamolin, “Three-dimensional structural optimization of controlled rigid motion in a resisting medium,” in: Proc. WCSMO-2, Zakopane, Poland, May 26-30, 1997, Zakopane, Poland (1997), pp. 387-392.
[221]	M. V. Shamolin, “Some classical problems in three-dimensional dynamics of a rigid body interacting with a medium,” in: Proc. ICTACEM98, Kharagpur, India, December 1-5, 1998, Indian Inst. Technology, Kharagpur, India (1998), pp. 1-11.
[222]	M. V. Shamolin, “Mathematical modelling of interaction of a rigid body with a medium and new cases of integrability,” in: CD Proc. ECCOMAS 2000, Barcelona, Spain, September 11-14, Barcelona (2000), pp. 1-11.
[223]	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) · Zbl 1006.34035 · doi:10.1023/A:1015026512786
[224]	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 · doi:10.1023/A:1021865626829
[225]	Shamolin, MV, Foundations of differential and topological diagnostics, J. Math. Sci., 114, 976-1024, (2003) · Zbl 1067.93020 · doi:10.1023/A:1021807110899
[226]	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 · doi:10.1023/B:JOTH.0000029572.16802.e6
[227]	M. V. Shamolin, “Structural stable vector fields in rigid body dynamics,” in: Proc. 8th Conf. Dynamical Systems: Theory and Applications (DSTA 2005), Lodz, Poland, December 12-15, 2005, 1, Technical Univ. Lodz (2005), pp. 429-436.
[228]	M. V. Shamolin, “The cases of integrability in terms of transcendental functions in dynamics of a rigid body interacting with a medium,” in: Proc. 9th Conf. Dynamical Systems: Theory and Applications (DSTA 2007), Lodz, Poland, December 17-20, 2007, 1, Technical Univ. Lodz (2007), pp. 415-422.
[229]	Shamolin, MV, Some methods of analysis of the dynamic systems with various dissipation in dynamics of a rigid body, Proc. Appl. Math. Mech., 8, 10137-10138, (2008) · Zbl 1393.37096 · doi:10.1002/pamm.200810137
[230]	M. V. Shamolin, “Dynamical systems with variable dissipation: Methods and applications,” in: Proc. 10th Conf. Dynamical Systems: Theory and Applications (DSTA 2009), Lodz, Poland, December 7-10, 2009, Technical Univ. Lodz (2009), pp. 91-104.
[231]	M. V. Shamolin, “The various cases of complete integrability in dynamics of a rigid body interacting with a medium,” in: CD Proc. Conf. Multibody Dynamics, ECCOMAS Thematic Conf. Warsaw, Poland, June 29-July 2, 2009, Polish Acad. Sci., Warsaw (2009), pp. 1-20.
[232]	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) · doi:10.1002/pamm.200910044
[233]	M. V. Shamolin, “Dynamical systems with various dissipation: Background, methods, applications,“ in: CD Proc. XXXVIII Summer School-Conf. “Advanced Problems in Mechanics” (APM 2010), July 1-5, 2010, St. Petersburg (Repino), Russia [in Russian], St. Petersburg (2010), pp. 612-621.
[234]	Shamolin, MV, Integrability and nonintegrability in terms of transcendental functions in dynamics of a rigid body, Proc. Appl. Math. Mech., 10, 63-64, (2010) · doi:10.1002/pamm.201010024
[235]	M. V. Shamolin, “Cases of complete integrability in transcendental functions in dynamics and certain invariant indices,” in: CD Proc. 5th Int. Sci. Conf. Physics and Control PHYSCON 2011, Leon, Spain, September 5-8, 2011, Leon, Spain (2011) pp. 1-5.
[236]	M. V. Shamolin, “Variety of the cases of integrability in dynamics of a 2D-, 3D-, and 4Drigid body interacting with a medium,” in: Proc. 11th Conf. Dynamical Systems: Theory and Applications (DSTA 2011), Lodz, Poland, December 5-8, 2011, Technical Univ. Lodz (2011), pp. 11-24.
[237]	Shamolin, MV, Cases of complete integrability in transcendental functions in dynamics and certain invariant indices, Proc. Appl. Math. Mech., 12, 43-44, (2012) · doi:10.1002/pamm.201210013
[238]	M. V. Shamolin, “Cases of integrability in transcendental functions in 3D Dynamics of a rigid body interacting with a medium,” in: Proc. ECCOMAS Multibody Dynamics 2013, Zagreb, Croatia, July 1-4, 2013, Zagreb, University of Zagreb (2013), pp. 903-912.
[239]	Shamolin, MV, Variety of the cases of integrability in dynamics of a symmetric 2D-, 3D- and 4D-rigid body in a nonconservative field, Int. J. Struct. Stabil. Dynam., 13, 1340011-1340024, (2013) · Zbl 1359.70059 · doi:10.1142/S0219455413400117
[240]	M. V. Shamolin, “Review of cases of integrability in dynamics of lower- and multidimensional rigid body in a nonconservative field of forces,” in: Proc. 2014 Int. Conf. on Pure Mathematics and Applied Mathematics (PMAM’14), Venice, Italy, March 15-17, 2014, Venice (2014), pp. 86-102.
[241]	M. V. Shamolin, “New cases of integrability in multidimensional dynamics in a nonconservative field,“ in: CD Proc. XLII Summer School-Conf. “Advanced Problems in Mechanics” (APM 2014), June 30-July 5, 2014, St. Petersburg (Repino), Russia [in Russian], St. Petersburg (2014), pp. 435-446.
[242]	M. V. Shamolin, “Dynamical pendulum-like nonconservative systems,” in: Applied Non-Linear Dynamical Systems, Springer Proc. Math. Stat., 93, 503-525 (2014). · Zbl 1302.70051
[243]	Shamolin, MV, On stability of certain key types of rigid body motion in a nonconservative field, Proc. Appl. Math. Mech., 14, 311-312, (2014) · doi:10.1002/pamm.201410143
[244]	Shamolin, MV, Classification of integrable cases in the dynamics of a four-dimensional rigid body in a nonconservative field in the presence of a tracking force, J. Math. Sci., 204, 808-870, (2015) · Zbl 1346.70007 · doi:10.1007/s10958-015-2220-0
[245]	M. V. Shamolin, “Certain Integrable Cases in Dynamics of a Multi-Dimensional Rigid Body in a Nonconservative Field,” in: Proc. Int. Conf. on Pure and Appl. Math. (PMAM’15), Vienna, Austria, March 15-17, 2015, Vienna (2015), pp. 328-342.
[246]	M. V. Shamolin, “Multidimensional pendulum in a nonconservative force field,“ in: CD Proc. XLIII Summer School-Conf. “Advances Problems in Mechanics” (APM 2015), June 22-27, 2015, St. Petersburg, Russia [in Russian], St. Petersburg (2015), pp. 322-332.