A specific example in which the theory developed here is quite crucial is the analysis of locomotion for the snakeboard, which we study in some detail in Section . The snakeboard is a modified version of a skateboard in which locomotion is achieved by using a coupling of the nonholonomic constraints with the symmetry properties of the system. For that system, traditional analysis of the complete dynamics of the system does not readily explain the mechanism of locomotion. By means of the momentum equation which we derive in this paper, the interaction between the constraints and the symmetries becomes quite clear and the basic mechanics underlying locomotion is.
