This article is cited in 6 papers

On the Normal Force and Static Friction Acting on a Rolling Ball Actuated by Internal Point Masses

Vakhtang Putkaradze^a, Stuart M. Rogers<sup>b

a</sup> Department of Mathematical and Statistical Sciences, Faculty of Science, University of Alberta, CAB 632, Edmonton, AB T6G 2G1, Canada
^b Institute for Mathematics and its Applications, College of Science and Engineering, University of Minnesota, 207 Church Street SE, 306 Lind Hall, Minneapolis, MN 55455, USA

Abstract: 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.

Keywords: nonholonomic mechanics, holonomic mechanics, rolling balls, rolling disks.

MSC: 37J60, 70E18, 70E60

Received: 06.10.2018
Accepted: 17.09.2019

Language: English

DOI: 10.1134/S1560354719020023

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