A related modern example is the snakeboard (see LEWIS,OSTROWSKI,MURRAY &BURDICK [1994]),which shares some of the features of these examples butwhich has a crucial difference as well. This example, likemany of the others, has the sym- metry group SE(2) of Euclidean motions of the plane but, now, the corresponding momentum is not conserved. However, the equation satisfied by the momentum associated with the symmetry is useful for understanding the dynamics of the prob- lem and how group motion can be generated. The nonconservation of momentum occurs even with no forces applied (besides the forces of constraint) and is consis- tent with the conservation of energy for these systems. In.
