Nonholonomic systems are an active field of research both in dynamical systems and in geometric control theory. A mechanical systems is called nonholonomic if constraints on the velocities are allowed. Nonholonomic affine constraints on the velocities have been recently introduced and studied, in particular in relation on the non-conservation of the mechanical energy. Even if the energy is not usually conserved it may happen that a modification of it, called “moving energy”, is conserved. In this project we aim to investigate the relation of the conservation of the moving energy with the presence of symmetries.
