Hamel’s Formalism for Classical Field Theories

This paper introduces Hamel’s formalism for classical field theories with the goal of analyzing the dynamics of continuum mechanical systems with velocity constraints. The developed formalism is utilized to prove the existence and uniqueness of motions of an infinite-dimensional generalization of the Chaplygin sleigh, a canonical example of nonholonomic dynamics. The formalism is very flexible and, for mechanical field theories, includes the Eulerian and Lagrangian representations of continuum mechanics as special cases. It also provides a useful approach to analyzing symmetry reduction.