A class of nonholonomic kinematic constraints in elasticity

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.

28 pages, 7 figures, uses IOPP LaTeX style (included) (v3: section 2 entirely rewritten)

References in corpus (4)

• Momentum Maps and Classical Relativistic Fields. Part II: Canonical Analysis of Field Theories
• Geometric Structures in Field Theory
• The momentum map for nonholonomic field theories with symmetry
• Chetaev vs. vakonomic prescriptions in constrained field theories with parametrized variational calculus

Cited by in corpus (2)

• Symmetry aspects of nonholonomic field theories
• Nonholonomic constraints in $k$-symplectic Classical Field Theories