Voir la notice de l'article provenant de la source Math-Net.Ru
@article{SJIM_2020_23_4_a10, author = {M. V. Shamolin}, title = {Families of portraits of some pendulum-like systems in dynamics}, journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki}, pages = {144--156}, publisher = {mathdoc}, volume = {23}, number = {4}, year = {2020}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/SJIM_2020_23_4_a10/} }
M. V. Shamolin. Families of portraits of some pendulum-like systems in dynamics. Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 4, pp. 144-156. http://geodesic.mathdoc.fr/item/SJIM_2020_23_4_a10/
[1] H. Poincaré, On curves defined by differential equations, OGIZ, M.–L., 1947 (in Russian)
[2] M. V. Shamolin, “Dynamical systems with various dissipation: background, methods, and applications”, Fundament. i Prikl. Matematika, 14:3 (2008), 3–237 (in Russian) | MR
[3] I. Bendikson, “About curves defined by differential equations”, Uspekhi Mat. Nauk, 1941, no. 9, 119–211 (in Russian)
[4] A. D. Bryuno, The local method of nonlinear analysis of differential equations, Nauka, M., 1979 (in Russian)
[5] V. V. Golubev, Lectures on integration of the equations of motion of a rigid body about a fixed point, Gostekhizdat, M., 1953 (in Russian) | MR
[6] C. Jakobi, Lectures on Dynamics, 1936, ONTI, M. (in Russian)
[7] B. Ya. Lokshin, V. A. Samsonov, M. V. Shamolin, “Pendulum systems with dynamical symmetry”, Sovrem. Mat. i Ee Prilozhen., 100 (2016), 76–133 (in Russian)
[8] M. V. Shamolin, “Application of the methods of topographic Poincaré systems and comparison systems to some particular systems of differential equations”, Vestnik MGU. Ser. 1. Mat. Mekh., 1993, no. 2, 66–70 (in Russian) | MR | Zbl
[9] M. I. Gurevich, Theory of jets in ideal fluids, Nauka, M., 1979 (in Russian)
[10] S. A. Chaplygin, On motion of heavy bodies in an incompressible fluid, v. 1, Izd. Akad. Nauk SSSR, L., 1933, 133–135 (in Russian)
[11] S. A. Chaplygin, Selected works, Nauka, M., 1976 (in Russian) | MR
[12] V. A. Samsonov, M. V. Shamolin, “Body motion in a resisting medium”, Vestnik MGU. Ser. 1. Mat. Mekh., 1989, no. 3, 51–54 (in Russian) | Zbl
[13] M. V. Shamolin, “Phase pattern classification for the problem of the motion of a body in a resisting medium in the presence of a linear damping moment”, J. Appl. Math. Mech., 57:4 (1993), 623–632 | DOI | MR | Zbl
[14] M. V. Shamolin, “Comparison of Jacobi integrable cases of plane and spatial motion of a body in a medium at streamlining”, J. Appl. Math. Mech., 69:6 (2005), 900–906 | DOI | MR | Zbl
[15] M. V. Shamolin, “On the problem of the motion of a body in a resistant medium”, Moscow Univ. Mech. Bull., 47:1 (1992), 4–10 | MR | Zbl | Zbl
[16] M. V. Shamolin, “Existence and uniqueness of trajectories that have points at infinity as limit sets for dynamical systems on the plane”, Moscow Univ. Mech. Bull., 48:1 (1993), 1–6 | MR | Zbl
[17] V. A. Pliss, Integral sets of periodical systems of differential equations, Nauka, M., 1967 (in Russian)
[18] B. V. Shabat, Introduction to complex analysis, Nauka, M., 1987 (in Russian)
[19] V. G. Tabachnikov, “Stationary characteristics of wings at slow speeds in the whole range of angles of incidence”, Trudy TsAGI, 1621 (1974), 18–24 (in Russian)
[20] B. Ya. Lokshin, V. A. Privalov, V. A. Samsonov, Introduction to the problem of motion of a rigid body in a resistant medium, Publ. Moskov. Gos. Univ., M., 1986 (in Russian)
[21] M. V. Shamolin, “Spatial topographical systems of Poincaré and comparison systems”, Russian Math. Surveys, 52:3 (1997), 621–622 | DOI | MR | Zbl
[22] M. V. Shamolin, “On integrability in transcendental functions”, Russian Math. Surveys, 53:3 (1998), 637–638 | DOI | MR | Zbl
[23] N. Bourbaki, Integration, Nauka, M., 1970 (in Russian) | MR
[24] V. V. Golubev, Lectures on analytical theory of differential equations, Gostekhizdat, M.–L., 1950 (in Russian) | MR
[25] B. A. Dubrovin, S. P. Novikov, A. T. Fomenko, Modern geometry, Nauka, M., 1979 (in Russian) | MR
[26] G. Lamb, Hydrodynamics, Fizmatgiz, M., 1947 (in Russian)
[27] M. V. Shamolin, “Different topological types of trajectories in the problem of body motion in a resisting medium”, Moscow Univ. Mech. Bull., 47:2 (1992), 13–16 | MR | Zbl
[28] M. V. Shamolin, “Three-parametric family of phase portraits in dynamics of a solid interacting with a medium”, Dokl. Phys., 53:1 (2008), 23–28 | DOI | MR | Zbl
[29] M. V. Shamolin, “Multiparameter family of phase portraits in the dynamics of a rigid body interacting with a medium”, Moscow Univ. Mech. Bull., 66:3 (2011), 49–55 | DOI | MR | Zbl