Аннотация:
In this paper the dynamics of a Chaplygin sleigh like system are investigated. The system consists a of a Chaplygin sleigh with an internal rotor connected by a torsional spring, which is possibly non-Hookean. The problem is motivated by applications in robotics, where the motion of a nonholonomic system is sought to be controlled by modifying or tuning the stiffness associated with some degrees of freedom of the system. The elastic potential modifies the dynamics of the system and produces two possible stable paths in the plane, a straight line and a circle, each of which corresponds to fixed points in a reduced velocity space. Two different elastic potentials are considered in this paper, a quadratic potential and a Duffing like quartic potential. The stiffness of the elastic element, the relative inertia of the main body and the internal rotor and the initial energy of the system are all bifurcation parameters. Through numerics, we investigate the codimension-one bifurcations of the fixed points while holding all the other bifurcation parameters fixed. The results show the possibility of controlling the dynamics of the sleigh and executing different maneuvers by tuning the stiffness of the spring.
Ключевые слова:
nonholonomic systems, Chaplygin sleigh, passive degrees of freedom.
Поступила в редакцию: 11.11.2018 Принята в печать: 04.01.2019
Образец цитирования:
Vitaliy Fedonyuk, Phanindra Tallapragada, “The Dynamics of a Chaplygin Sleigh with an Elastic Internal Rotor”, Regul. Chaotic Dyn., 24:1 (2019), 114–126
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\paper The Dynamics of a Chaplygin Sleigh with an Elastic Internal Rotor
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd393
https://www.mathnet.ru/rus/rcd/v24/i1/p114
Эта публикация цитируется в следующих 11 статьяx:
Junhong Li, Ning Cui, “Hyperchaos, constraints and its stability control in a 6D hyperchaotic particle motion system”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 238:5 (2024), 1234
Colin Rodwell, Phanindra Tallapragada, “Physics-informed reinforcement learning for motion control of a fish-like swimming robot”, Sci Rep, 13:1 (2023)
Elizaveta M. Artemova, Evgeny V. Vetchanin, “The Motion of an Unbalanced Circular Disk
in the Field of a Point Source”, Regul. Chaotic Dyn., 27:1 (2022), 24–42
Colin Rodwell, Phanindra Tallapragada, “Induced and tunable multistability due to nonholonomic constraints”, Nonlinear Dyn, 108:3 (2022), 2115
M. Z. Dosaev, L. A. Klimina, V. A. Samsonov, Yu. D. Selyutsky, “Plane-Parallel Motion of a Snake Robot in the Presence of Anisotropic Dry Friction and a Single Control Input”, J. Comput. Syst. Sci. Int., 61:5 (2022), 858
I. Bizyaev, S. Bolotin, I. Mamaev, “Normal forms and averaging in an acceleration problem in nonholonomic mechanics”, Chaos, 31:1 (2021), 013132
Alexander Kilin, Elena Pivovarova, 2021 International Conference “Nonlinearity, Information and Robotics” (NIR), 2021, 1
S. A. Emam, “Generalized Lagrange's equations for systems with general constraints and distributed parameters”, Multibody Syst. Dyn., 49:1 (2020), 95–117
А. А. Килин, Е. Н. Пивоварова, “Неинтегрируемость задачи о качении сферического волчка по вибрирующей плоскости”, Вестн. Удмуртск. ун-та. Матем. Мех. Компьют. науки, 30:4 (2020), 628–644
V. Fedonyuk, Ph. Tallapragada, “Locomotion of a compliant mechanism with nonholonomic constraints”, J. Mech. Robot., 12:5 (2020), 051006
Bizyaev I.A. Borisov A.V. Mamaev I.S., “Dynamics of a Chaplygin Sleigh With An Unbalanced Rotor: Regular and Chaotic Motions”, Nonlinear Dyn., 98:3 (2019), 2277–2291
Цитирование в формате AMSBIB
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