Abstract:
A heavy balanced nonhomogeneous ball moving on a rough horizontal plane is considered. The classical model of a “marble” body means a single point of contact, where sliding is impossible. We suggest that the contact forces be described by Coulomb’s law and show that in the final motion there is no sliding. Another, relatively new, contact model is the “rubber” ball: there is no sliding and no spinning. We treat this situation by applying a local Coulomb law within a small contact area. It is proved that the final motion of a ball with such friction is the motion of the “rubber” ball.
\Bibitem{Iva16}
\by Alexander P. Ivanov
\paper On Final Motions of a Chaplygin Ball on a Rough Plane
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 7-8
\pages 804--810
\mathnet{http://mi.mathnet.ru/rcd226}
\crossref{https://doi.org/10.1134/S1560354716070030}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016028953}
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This publication is cited in the following 6 articles:
Firdaus E. Udwadia, Nami Mogharabin, “New Directions in Modeling and Computational Methods for Complex Mechanical Dynamical Systems”, Processes, 10:8 (2022), 1560
F. E. Udwadia, N. Mogharabin, “The use of zero-mass particles in analytical and multi-body dynamics: sphere rolling on an arbitrary surface”, J. Appl. Mech.-Trans. ASME, 88:12 (2021), 121006
A. P. Ivanov, “On singular points of equations of mechanics”, Dokl. Math., 97:2 (2018), 167–169
A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840
A. V. Borisov, A. O. Kazakov, E. N. Pivovarova, “Regulyarnaya i khaoticheskaya dinamika v «rezinovoi» modeli volchka Chaplygina”, Nelineinaya dinam., 13:2 (2017), 277–297
Alexey V. Borisov, Alexey O. Kazakov, Elena N. Pivovarova, “Regular and Chaotic Dynamics in the Rubber Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 885–901
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