Jerky Motion of Active Granular Particles

Abstract

Abrupt transitions between rest and motion can render the standard Newtonian description -- based on position, velocity, and acceleration -- incomplete, requiring higher-order derivatives such as the jerk, the third time derivative of position. Here, we show that the interplay between activity and dry friction gives rise to robust jerk-dominated dynamics in self-propelled particles: the particle speed increases quadratically with time under an active force, in contrast to the linear growth expected for conventional Newtonian dynamics. We demonstrate this behavior analytically, numerically, and experimentally using active vibrobots self-propelling on a vertically vibrating plate at low vibration amplitudes, where surface asperities generate dry friction and, thus, give rise to jerky motion when combined with activity. Our results establish dry friction as a simple mechanism for realizing higher-order dynamics in active matter and suggest that jerky dynamics may arise broadly in nonequilibrium systems with frictional contacts.