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

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 $t_{\text{f}}$ depends on the circular driving frequency $\omega$, unlike the viscous case previously studied. We find $t_{\text{f}}\sim {\omega }^{\gamma -1}{\mu }^{-\gamma /2}$, 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 $H_{\text{c}}(\mu )$ where RRs become possible follows a $q$-exponential with $q\simeq 1.9$, 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.

arXiv comment11 pages, 10 figures

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