A geometrical framework for the study of non-holonomic Lagrangian systems: II

A Lagrangian system subject to linear non-holonomic constraints may be represented in several different geometrical frameworks. We describe one such framework, involving the addition of an extra term to the Cartan 2-form of the unconstrained system, which is dual to the traditional approach of adding a reaction force to the unconstrained dynamical vector field . We show how this framework is closely related to the method of constructing a 2-form when the constraints are given by a connection on an auxiliary bundle, as described in our earlier work.