Pick-up and impact of flexible bodies

TL;DR

This paper analyzes the dynamics of flexible bodies during partial-contact interactions, deriving energy and momentum balances, and reveals an asymmetry in pick-up versus lay-down processes supported by experiments.

Contribution

It introduces a novel framework for understanding moving discontinuities in flexible bodies, including energy dissipation and asymmetries in contact processes.

Findings

Asymmetry between pick-up and lay-down processes in strings.

Compatibility relation between momentum and energy supplies.

Experimental validation of the predicted asymmetry.

Abstract

Picking up, laying down, colliding, rolling, and peeling are partial-contact interactions involving moving discontinuities. We examine the balances of momentum and energy across a moving discontinuity in a string, with allowance for injection or dissipation by singular supplies. We split the energy dissipation according to its invariance properties, discuss analogies with systems of particles and connections with the literature on shocks and phase transition fronts in various bodies, and derive a compatibility relation between supplies of momentum and translation-invariant energy. For a moving contact discontinuity between a string and a smooth rigid plane in the presence of gravity, we find a surprising asymmetry between the processes of picking up and laying down, such that steady-state kinks in geometry and associated jumps in tension are not admissible during pick-up. This prediction is consistent with experimental observations. We briefly discuss related problems including the falling folded chain, peeling of an adhesive tape, and the "chain fountain". Our approach is applicable to the study of impact and locomotion, and to systems such as moored floating structures and some musical instruments that feature vibrating string and cable elements interacting with a surface.