This work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of Lagrangian me- chanics and with a view to control-theoretical applications. The basic methodology is that of geometric mechanics applied to the Lagrange-d’Alembert formulation, generalizing the use of connections and momentum maps associated with a given symmetry group to this case. We begin by formulating the mechanics of nonholo- nomic systems using an Ehresmann connection to model the constraints, and show how the curvature of this connection enters into Lagrange’s equations. Unlike the situationwith standard configuration-space constraints, the presence of symmetries in the nonholonomic case may or may not lead to.
