Аннотация:
In this paper we develop a new model of non-holonomic billiard that accounts for the intrinsic rotation of the billiard ball. This model is a limit case of the problem of rolling without slipping of a ball without slipping over a quadric surface. The billiards between two parallel walls and inside a circle are studied in detail. Using the three-dimensional-point-map technique, the non-integrability of the non-holonomic billiard within an ellipse is shown.
Ключевые слова:
billiard, impact, point map, nonintegrability, periodic solution, nonholonomic constraint, integral of motion.
Поступила в редакцию: 06.11.2010 Принята в печать: 14.07.2011
Образец цитирования:
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “On the Model of Non-holonomic Billiard”, Regul. Chaotic Dyn., 16:6 (2011), 653–662
\RBibitem{BorKilMam11}
\by Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev
\paper On the Model of Non-holonomic Billiard
\jour Regul. Chaotic Dyn.
\yr 2011
\vol 16
\issue 6
\pages 653--662
\mathnet{http://mi.mathnet.ru/rcd461}
\crossref{https://doi.org/10.1134/S1560354711060062}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd461
https://www.mathnet.ru/rus/rcd/v16/i6/p653
Эта публикация цитируется в следующих 5 статьяx:
Vladimir Dragović, Sean Gasiorek, Milena Radnović, “Billiard Ordered Games and Books”, Regul. Chaotic Dyn., 27:2 (2022), 132–150
G. R. Saypulaev, B. I. Adamov, A. I. Kobrin, “Comparative Analysis of the Dynamics of a Spherical
Robot with a Balanced Internal Platform Taking into
Account Different Models of Contact Friction”, Rus. J. Nonlin. Dyn., 18:5 (2022), 803–815
J. Ahmed, C. Cox, B. Wang, “No-slip billiards with particles of variable mass distribution”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 32:2 (2022)
Christopher Cox, Renato Feres, Bowei Zhao, “Rolling Systems and Their Billiard Limits”, Regul. Chaotic Dyn., 26:1 (2021), 1–21
А. В. Борисов, И. С. Мамаев, А. В. Цыганов, “Неголономная динамика и пуассонова геометрия”, УМН, 69:3(417) (2014), 87–144; A. V. Borisov, I. S. Mamaev, A. V. Tsiganov, “Non-holonomic dynamics and Poisson geometry”, Russian Math. Surveys, 69:3 (2014), 481–538
Цитирование в формате AMSBIB
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