Abstract:
The motion of a spherical robot with periodically changing moments of inertia, internal rotors and a displaced center of mass is considered. It is shown that, under some restrictions on the displacement of the center of mass, the system of interest features chaotic dynamics due to separatrix splitting. A stability analysis is made of the upper equilibrium point of the ball and of the periodic solution arising in its neighborhood, in the case of periodic rotation of the rotors. It is shown that the lower equilibrium point can become unstable in the case of fixed rotors and periodically changing moments of inertia.
Keywords:
nonholonomic constraint, rubber rolling, unbalanced ball, rolling on a plane.
The work of E.M.Artemova (Section 3) was carried out within the framework of the state
assignment of the Ministry of Science and Higher Education of Russia (Project FEWS-2020-0009).
The work of Yu. L. Karavaev (Introduction and Section 2) was supported by the Russian Science
Foundation under grant 18-71-00096.
The work of I. S.Mamaev (Section 5) was carried out within the framework of the state
assignment of the Ministry of Science and Higher Education of Russia (Project FZZN-2020-0011)
The work of E.V.Vetchanin (Section 4) was supported by the Russian Science Foundation under
grant 18-71-00111.
Citation:
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
\Bibitem{ArtKarMam20}
\by Elizaveta M. Artemova, Yury L. Karavaev, Ivan S. Mamaev, Evgeny V. Vetchanin
\paper Dynamics of a Spherical Robot with Variable Moments of Inertia and a Displaced Center of Mass
\jour Regul. Chaotic Dyn.
\yr 2020
\vol 25
\issue 6
\pages 689--706
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Linking options:
https://www.mathnet.ru/eng/rcd1091
https://www.mathnet.ru/eng/rcd/v25/i6/p689
This publication is cited in the following 9 articles:
Alexander A. Kilin, Elena N. Pivovarova, “Bifurcation analysis of the problem of a “rubber” ellipsoid of revolution rolling on a plane”, Nonlinear Dyn, 2024
V. D. Anisimov, A. G. Egorov, A. N. Nuriev, O. N. Zaitseva, “Propulsive Motion of Cylindrical Vibration-Driven Robot in a Viscous Fluid”, jour, 166:3 (2024), 277
A. V. Klekovkin, Yu. L. Karavaev, A. V. Nazarov, “Stabilization of a Spherical Robot with an Internal Pendulum During Motion on an Oscillating Base”, Rus. J. Nonlin. Dyn., 20:5 (2024), 845–858
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
E. M. Artemova, A. A. Kilin, Yu. V. Korobeinikova, “Issledovanie orbitalnoi ustoichivosti pryamolineinykh kachenii roller-reisera po vibriruyuschei ploskosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:4 (2022), 615–629
E. V. Vetchanin, I. S. Mamaev, “Chislennyi analiz periodicheskikh upravlenii vodnogo robota neizmennoi formy”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:4 (2022), 644–660
Alexander P. Ivanov, “Singularities in the rolling motion of a spherical robot”, International Journal of Non-Linear Mechanics, 145 (2022), 104061
Alexander A. Kilin, Elena N. Pivovarova, “Motion control of the spherical robot rolling on a vibrating plane”, Applied Mathematical Modelling, 109 (2022), 492
Evgeny V. Vetchanin, 2021 International Conference “Nonlinearity, Information and Robotics” (NIR), 2021, 1
Citation in format AMSBIB
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