Аннотация:
The goal of this paper is to investigate the normal and tangential forces acting at the point of contact between a horizontal surface and a rolling ball actuated by internal point masses moving in the ball’s frame of reference. The normal force and static friction are derived from the equations of motion for a rolling ball actuated by internal point masses that move inside the ball’s frame of reference, and, as a special case, a rolling disk actuated by internal point masses. The masses may move along one-dimensional trajectories fixed in the ball’s and disk’s frame. The dynamics of a ball and disk actuated by masses moving along one-dimensional trajectories are simulated numerically and the minimum coefficients of static friction required to prevent slippage are computed.
Ключевые слова:
nonholonomic mechanics, holonomic mechanics, rolling balls, rolling disks.
Финансовая поддержка
Vakhtang Putkaradze’s research was partially supported by an NSERC Discovery Grant and the University of Alberta. Stuart Rogers’ postdoctoral research was supported by Target Corporation and the Institute for Mathematics and its Applications at the University of Minnesota.
Поступила в редакцию: 06.10.2018 Принята в печать: 17.09.2019
Образец цитирования:
Vakhtang Putkaradze, Stuart M. Rogers, “On the Normal Force and Static Friction Acting on a Rolling Ball Actuated by Internal Point Masses”, Regul. Chaotic Dyn., 24:2 (2019), 145–170
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd450
https://www.mathnet.ru/rus/rcd/v24/i2/p145
Эта публикация цитируется в следующих 6 статьяx:
Yu. L. Karavaev, “Spherical Robots:
An Up-to-Date Overview of Designs and Features”, Rus. J. Nonlin. Dyn., 18:4 (2022), 709–750
V. Putkaradze, S. Rogers, “Numerical simulations of a rolling ball robot actuated by internal point masses”, Numer. Algebr. Control Optim., 11:2 (2021), 143–207
Alexander Kilin, Elena Pivovarova, 2021 International Conference “Nonlinearity, Information and Robotics” (NIR), 2021, 1
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
V. Putkaradze, S. Rogers, “On the optimal control of a rolling ball robot actuated by internal point masses”, J. Dyn. Syst. Meas. Control-Trans. ASME, 142:5 (2020)
Цитирование в формате AMSBIB
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