A class of nonholonomic kinematic constraints in elasticity

TL;DR

This paper introduces a novel classical field theory with nonholonomic constraints, modifying a Cosserat rod model, and develops a geometric integration scheme for its dynamics.

Contribution

It presents the first example of a simple classical field theory with nonholonomic constraints and a geometric integration method for its dynamics.

Findings

Derived equations of motion for the constrained model

Proposed a geometric integration scheme

Demonstrated the model's consistency with nonholonomic constraints

Abstract

We propose a first example of a simple classical field theory with nonholonomic constraints. Our model is a straightforward modification of a Cosserat rod. Based on a mechanical analogy, we argue that the constraint forces should be modeled in a special way, and we show how such a procedure can be naturally implemented in the framework of geometric field theory. Finally, we derive the equations of motion and we propose a geometric integration scheme for the dynamics of a simplified model.