Nonholonomic reduction
This paper addresses the problem of nonholonomic reduction of Hamiltonian systems in the presence of symmetry. The authors describe the structure of Hamiltonian systems with constraints in a manner that facilitates understanding of the reduction process. For simplicity of exposition, the authors examine only Hamiltonian systems that come from a Lagrangian system (of the form kinetic energy minus potential energy) where the Legendre transformation is a diffeomorphism and the constraints are independent of time. The reduction of nonholonomic systems by symmetry is formulated in such a way that it parallels the standard theory of reduction of symplectic manifolds with symmetry. In so doing, the authors show that the constraints in the Hamiltonian theory play a dual role in which they define both a constraint manifold and a horizontal distribution on which a distributional form of Hamilton's equations hold. The authors illuminate their results using the example of a free particle subjected to a nonholonomic constraint.
scientific article; zbMATH DE number 563469