Аннотация:
In this paper we consider the problem of the motion of the Roller Racer. We assume that the angle φ(t) between the platforms is a prescribed function of time. We prove that in this case the acceleration of the Roller Racer is unbounded. In this case, as the Roller Racer accelerates, the increase in the constraint reaction forces is also unbounded. Physically this means that, from a certain instant onward, the conditions of the rolling motion of the wheels without slipping are violated. Thus, we consider a model in which, in addition to the nonholonomic constraints, viscous friction force acts at the points of contact of the wheels. For this case we prove that there is no constant acceleration and all trajectories of the reduced system asymptotically tend to a periodic solution.
The work of I.A. Bizyaev (Sections 1 and 3) was supported by the RFBR grant No. 18-38-00344 mol_a and was carried out at MIPT under project 5–100 for state support for leading universities of the Russian Federation. The work of A.V. Borisov (Section 2) was supported by the RFBR grant no. 18-08-00999-a. The work of I.S. Mamaev (Section 4) was carried out within the framework of the state assignment of the Ministry of Education and Science of Russia (1.2405.2017/4.6).
Поступила в редакцию: 17.09.2018 Принята в печать: 20.10.2018
Образец цитирования:
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Exotic Dynamics of Nonholonomic Roller Racer with Periodic Control”, Regul. Chaotic Dyn., 23:7-8 (2018), 983–994
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\paper Exotic Dynamics of Nonholonomic Roller Racer with Periodic Control
\jour Regul. Chaotic Dyn.
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\vol 23
\issue 7-8
\pages 983--994
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https://www.mathnet.ru/rus/rcd379
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Эта публикация цитируется в следующих 27 статьяx:
Ivan A. Bizyaev, Ivan S. Mamaev, “Roller Racer with Varying Gyrostatic Momentum:
Acceleration Criterion and Strange Attractors”, Regul. Chaotic Dyn., 28:1 (2023), 107–130
A. A. Kilin, T. B. Ivanova, “The Integrable Problem of the Rolling Motion
of a Dynamically Symmetric Spherical Top
with One Nonholonomic Constraint”, Rus. J. Nonlin. Dyn., 19:1 (2023), 3–17
Е. М. Артемова, А. А. Килин, Ю. В. Коробейникова, “Исследование орбитальной устойчивости прямолинейных качений роллер-рейсера по вибрирующей плоскости”, Вестн. Удмуртск. ун-та. Матем. Мех. Компьют. науки, 32:4 (2022), 615–629
E. M. Artemova, A. A. Kilin, “A Nonholonomic Model and Complete Controllability
of a Three-Link Wheeled Snake Robot”, Rus. J. Nonlin. Dyn., 18:4 (2022), 681–707
Alexander Kilin, Yuriy Karavaev, Kirill Yefremov, Lecture Notes in Networks and Systems, 324, Robotics for Sustainable Future, 2022, 428
Oriel Halvani, Yizhar Or, “Nonholonomic dynamics of the Twistcar vehicle: asymptotic analysis and hybrid dynamics of frictional skidding”, Nonlinear Dyn, 107:4 (2022), 3443
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
Alexander A. Kilin, Elena N. Pivovarova, “A Particular Integrable Case in the Nonautonomous Problem
of a Chaplygin Sphere Rolling on a Vibrating Plane”, Regul. Chaotic Dyn., 26:6 (2021), 775–786
E. A. Mikishanina, “Qualitative Analysis of the Dynamics of a Trailed
Wheeled Vehicle with Periodic Excitation”, Rus. J. Nonlin. Dyn., 17:4 (2021), 437–451
A. V. Borisov, A. V. Tsiganov, E. A. Mikishanina, “On inhomogeneous nonholonomic Bilimovich system”, Commun. Nonlinear Sci. Numer. Simul., 94 (2021), 105573
I. Bizyaev, S. Bolotin, I. Mamaev, “Normal forms and averaging in an acceleration problem in nonholonomic mechanics”, Chaos, 31:1 (2021), 013132
E A Mikishanina, “Two problems of movement of multi-link wheeled vehicles”, J. Phys.: Conf. Ser., 2094:2 (2021), 022063
Alexander Kilin, Elena Pivovarova, 2021 International Conference “Nonlinearity, Information and Robotics” (NIR), 2021, 1
Ivan S. Mamaev, Evgeny V. Vetchanin, “Dynamics of Rubber Chaplygin Sphere under Periodic Control”, Regul. Chaotic Dyn., 25:2 (2020), 215–236
Elizaveta M. Artemova, Yury L. Karavaev, Ivan S. Mamaev, Evgeny V. Vetchanin, “Dynamics of a Spherical Robot with Variable Moments of Inertia and a Displaced Center of Mass”, Regul. Chaotic Dyn., 25:6 (2020), 689–706
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
A. V. Borisov, E. A. Mikishanina, S. V. Sokolov, “Dynamics of multi-link uncontrolled wheeled vehicle”, Russ. J. Math. Phys., 27:4 (2020), 433–445
A. V. Tsiganov, “On a time-dependent nonholonomic oscillator”, Russ. J. Math. Phys., 27:3 (2020), 399–409
Elizaveta M. Artemova, Alexander A. Kilin, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1
Kirill S. Yefremov, Tatiana B. Ivanova, Alexander A. Kilin, Yury L. Karavaev, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1
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