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 (12)

• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• Variational methods, multisymplectic geometry and continuum mechanics
• Multisymplectic geometry, covariant Hamiltonians, and water waves
• Momentum Maps and Classical Relativistic Fields. Part II: Canonical Analysis of Field Theories
• Second-order multisymplectic field theory: A variational approach to second-order multisymplectic field theory
• Symmetries in Classical Field Theory
• Geometric Structures in Field Theory
• Discrete Lagrangian field theories on Lie groupoids
• Geometric aspects of nonholonomic field theories
• Nonholonomic constraints in classical field theories
• The momentum map for nonholonomic field theories with symmetry
• Chetaev vs. vakonomic prescriptions in constrained field theories with parametrized variational calculus

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• Multi-Dirac Structures and Hamilton-Pontryagin Principles for Lagrange-Dirac Field Theories
• Nonholonomic constraints in $k$-symplectic Classical Field Theories