Dynamics of elastic rods in perfect friction contact

TL;DR

This paper investigates the complex dynamics of elastic rods in perfect rolling contact, deriving equations of motion that reveal nonlinear behavior due to moving contact points, relevant for rods with rough surfaces.

Contribution

It introduces a novel analysis of elastic rod dynamics with perfect contact, avoiding potential-based models and highlighting nonlinear effects from moving contact points.

Findings

Derived equations of motion for rods with perfect rolling contact

Identified nonlinear behavior due to moving contact points

Revealed complex dynamics in systems with rough surface contact

Abstract

One of the most challenging and basic problems in elastic rod dynamics is a description of rods in contact that prevents any unphysical self-intersections. Most previous works addressed this issue through the introduction of short-range potentials. We study the dynamics of elastic rods with perfect rolling contact which is physically relevant for rods with rough surface, and cannot be described by any kind of potential. We derive the equations of motion and show that the system is essentially non-linear due to the moving contact position, resulting in a surprisingly complex behavior of the system.