Spinning rigid bodies driven by orbital forcing: The role of dry friction

TL;DR

This paper investigates how dry friction influences reverse rotation phenomena in spinning rigid bodies under orbital forcing, revealing transient behaviors, critical parameters, and the nonlinear dynamics involved.

Contribution

It introduces a detailed analysis of dry friction effects on reverse rotation, including the dependence of flip time on driving frequency and the conditions for reverse rotation occurrence.

Findings

Reverse rotations are transient and depend on initial conditions.

Flip time scales with frequency and friction coefficient as $t_f \\sim \\omega^{\\gamma-1} \\mu^{-\\\gamma/2}$.

Critical geometrical parameter $H_c$ follows a $q$-exponential distribution.

Abstract

A "circular orbital forcing" makes a chosen point on a rigid body follow a circular motion while the body spins freely around that point. We investigate this problem for the planar motion of a body subject to dry friction. We focus on the effect called reverse rotation (RR), where spinning and orbital rotations are antiparallel. Similar reverse dynamics include the rotations of Venus and Uranus, journal machinery bearings, tissue production reactors, and chiral active particles. Due to dissipation, RRs are possible only as a transient. Here the transient or flip time $t_\textrm{f}$ depends on the circular driving frequency $\omega$, unlike the viscous case previously studied. We find $t_\textrm{f}\sim\omega^{\gamma-1}\mu^{-\gamma/2}$, where $\mu$ is the friction coefficient and $\gamma=0$ ($\gamma=2$) for low (high) $\omega$. Whether RRs really occur depends on the initial conditions as well as on $\mu$ and $H$, a geometrical parameter. The critical $H_\textrm{c}(\mu)$ where RRs become possible follows a $q$-exponential with $q\simeq1.9$, a more restrictive RR scenario than in the wet case. We use animations to visualize the different dynamical regimes that emerge from the highly nonlinear dissipation mechanism of dry friction. Our results are valid across multiple investigated rigid body shapes.