Slipping and rolling on a rough accelerating surface

TL;DR

This paper analyzes the complex dynamics of objects slipping and rolling on rough surfaces that are either accelerating linearly or rotating, including effects of anisotropic friction and specific acceleration patterns.

Contribution

It provides a comprehensive study of slipping and rolling on accelerating and rotating rough surfaces, including anisotropic friction effects and specific acceleration cases.

Findings

Solutions relate sphere motion to point particle motion.

Periodic and sinusoidal accelerations lead to distinct motion patterns.

Anisotropic friction can cause stick-slip phenomena.

Abstract

The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and a sphere are studied, and it is shown that the solution to the latter problem can be expressed in terms of the solution to the former one. Examples of constant acceleration and periodic acceleration along a fixed line, and specifically sinusoidal acceleration along a fixed line, are studied in more detail. Also a situation is investigated where the friction is anisotropic, that is the friction coefficient depends on the direction of the velocity. In this situation, there may be stick-slip motions, and these are investigated in detail. For the second case, the motion of a point particle on a rough turntable is investigated.