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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
##### Keywords:
integrable cases; nonconservative force field
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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. 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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. 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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.
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