The Chaplygin sleigh with friction moving due to periodic oscillations of an internal mass

TL;DR

This paper investigates how internal mass oscillations can induce acceleration in a frictional Chaplygin sleigh, revealing mechanisms that lead to bounded or chaotic motion, including steady-state and random walk behaviors.

Contribution

It introduces two novel mechanisms for acceleration due to internal mass oscillations in a frictional sleigh, including parametric excitation effects and stabilization at certain velocities.

Findings

Acceleration can be induced by small oscillations in certain parameter regions.

Parametric excitation leads to bounded acceleration when oscillation line is displaced from the center.

Steady-state motion often exhibits chaotic attractors resembling random walks.

Abstract

For a Chaplygin sleigh moving in the presence of weak friction, we present and investigate two mechanisms of arising acceleration due to oscillations of an internal mass. In certain parameter regions, the mechanism induced by small oscillations determines acceleration which is on average one-directional. The role of friction is that the velocity reached in the process of the acceleration is stabilized at a certain level. The second mechanism is due to the effect of parametric excitation of oscillations, when the internal moving particle is comparable in mass with the main platform, and, as occurs, a necessary condition for the acceleration is presence of friction. The parametric instability and the resulting acceleration of the sleigh turn out to be bounded if the line of oscillations of the moving mass is displaced from the center of mass. The steady-state regime of motion is in many cases associated with a chaotic attractor; accordingly, the motion of the sleigh turns out to be similar to the process of random walk on a plane.