|
References
|
|
[1] |
Arnold, V. I., Ordinary Differential Equations, Springer, Berlin, 2006, ii+334 pp. |
[2] |
Bizyaev, I. A., Borisov, A. V., and Kuznetsov, S. P., “The Chaplygin Sleigh with Friction Moving due to Periodic Oscillations of an Internal Mass”, Nonlinear Dyn., 95:1 (2019), 699–714 |
[3] |
Bizyaev, I. A., Borisov, A. V., and Kuznetsov, S. P., “Chaplygin Sleigh with Periodically Oscillating Internal Mass”, Europhys. Lett., 119:6 (2017), 60008, 7 pp. |
[4] |
Bizyaev, I. A., Borisov, A. V., Kozlov, V. V., and Mamaev, I. S., “Fermi-Like Acceleration and Power-Law Energy Growth in Nonholonomic Systems”, Nonlinearity, 32:9 (2019), 3209–3233 |
[5] |
Bizyaev, I. A., Borisov, A. V., and Mamaev, I. S., “Exotic Dynamics of Nonholonomic Roller Racer with Periodic Control”, Regul. Chaotic Dyn., 23:7–8 (2018), 983–994 |
[6] |
Bolsinov, A. V. and Fomenko, A. T., Integrable Hamiltonian Systems: Geometry, Topology, Classification, Chapman & Hall/CRC, Boca Raton, Fla., 2004, xvi+730 pp. |
[7] |
Borisov, A. V., “On the Liouville Problem”, Numerical Modelling in the Problems of Mechanics, Mosk. Gos. Univ., Moscow, 1991, 110–118 (Russian) |
[8] |
Borisov, A. V., Kilin, A. A., and Mamaev, I. S., “Chaos in a Restricted Problem of Rotation of a Rigid Body with a Fixed Point”, Regul. Chaotic Dyn., 13:3 (2008), 221–233 |
[9] |
Borisov, A. V., Kilin, A. A., and Pivovarova, E. N., “Speedup of the Chaplygin Top by Means of Rotors”, Dokl. Phys., 64:3 (2019), 120–124 ; Dokl. Akad. Nauk, 485:3 (2019), 285–289 (Russian) |
[10] |
Borisov, A. V. and Kuznetsov, S. P., “Comparing Dynamics Initiated by an Attached Oscillating Particle for the Nonholonomic Model of a Chaplygin Sleigh and for a Model with Strong Transverse and Weak Longitudinal Viscous Friction Applied at a Fixed Point on the Body”, Regul. Chaotic Dyn., 23:7–8 (2018), 803–820 |
[11] |
Borisov, A. V. and Kuznetsov, S. P., “Regular and Chaotic Motions of Chaplygin Sleigh under Periodic Pulsed Torque Impacts”, Regul. Chaotic Dyn., 21:7–8 (2016), 792–803 |
[12] |
Borisov, A. V. and Mamaev, I. S., “Adiabatic Chaos in Rigid Body Dynamics”, Regul. Chaotic Dyn., 2:2 (1997), 65–78 (Russian) |
[13] |
Borisov, A. V. and Mamaev, I. S., “Euler – Poisson Equations and Integrable Cases”, Regul. Chaotic Dyn., 6:3 (2001), 253–276 |
[14] |
Borisov, A. V. and Mamaev, I. S., Rigid Body Dynamics: Hamiltonian Methods, Integrability, Chaos, R&C Dynamics, Institute of Computer Science, Izhevsk, 2005, 576 pp. (Russian) |
[15] |
Borisov, A. V., Mamaev, I. S., and Vetchanin, E. V., “Self-Propulsion of a Smooth Body in a Viscous Fluid under Periodic Oscillations of a Rotor and Circulation”, Regul. Chaotic Dyn., 23:7–8 (2018), 850–874 |
[16] |
Borisov, A. V., Mamaev, I. S., and Vetchanin, E. V., “Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation”, Regul. Chaotic Dyn., 23:4 (2018), 480–502 |
[17] |
Borisov, A. V. and Simakov, N. N., “A Computer “Proof” of Non-Integrability of Euler – Poisson Equations”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 1998, no. 1, 67–72 (Russian) |
[18] |
Butikov, E. I., “Stabilization of an Inverted Pendulum (60 Years of Kapitza Pendulum)”, Komput. Instr. v Obrazov., 2010, no. 5, 39–51 (Russian) |
[19] |
Doroshin, A. V., “Analysis of Attitude Motion Evolutions of Variable Mass Gyrostats and Coaxial Rigid Bodies System”, Internat. J. Non-Linear Mech., 45:2 (2010), 193–205 |
[20] |
Doroshin, A. V., Regular and Chaotic Dynamics of Satellite Gyrostats under Small Perturbations, Doctoral Dissertation, Samara Natl. Res. Univ., 2019, 224 pp. |
[21] |
Kharlamov, M. P., Topological Analysis of Integrable Problems of Rigid Body Dynamics, Leningr. Gos. Univ., Leningrad, 1988, 197 pp. (Russian) |
[22] |
Kilin, A. A. and Pivovarova, E. N., “Chaplygin Top with a Periodic Gyrostatic Moment”, Rus. J. Math. Phys., 25:4 (2018), 509–524 |
[23] |
Iñarrea, M. and Lanchares, V., “Chaos in the Reorientation Process of a Dual-Spin Spacecraft with Time-Dependent Moments of Inertia”, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10:5 (2000), 997–1018 |
[24] |
Iñarrea, M., Lanchares, V., Rothos, V. M., and Salas, J. P., “Chaotic Rotations of an Asymmetric Body with Time-Dependent Moments of Inertia and Viscous Drag”, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 13:2 (2003), 393–409 |
[25] |
Leonard, N. E., “Periodic Forcing, Dynamics and Control of Underactuated Spacecraft and Underwater Vehicles”, Proc. of the 34th IEEE Conf. on Decision and Control (New Orleans, La., Dec 1995), 3980–3985 |
[26] |
Mamaev, I. S. and Vetchanin, E. V., “The Self-Propulsion of a Foil with a Sharp Edge in a Viscous Fluid under the Action of a Periodically Oscillating Rotor”, Regul. Chaotic Dyn., 23:7–8 (2018), 875–886 |
[27] |
Tallapragada, P., “A Swimming Robot with an Internal Rotor As a Nonholonomic System”, American Control Conference (IEEE), 2015, 657-662 |
[28] |
Yakubovich, V. A. and Starzhinskii, V. M., Linear Differential Equations with Periodic Coefficients: In 2 Vols., Wiley, New York, 1975 |