Geometry of nonholonomic constraints

This paper presents a Hamiltonian treatment of nonholonomically constrained mechanical systems. We assume that the total energy of the systems is a sum of kinetic and potential energies and that the constraints are linear in velocities. We prove a nonholonomic version of Noetherʹs theorem and treat a special case of the nonholonomic reconstruction problem. The entire theory is illustrated by a disc, which rolls on a plane without slipping.