Nonlinear Superposition Formulas for Two Classes of Non-holonomic Systems

The aim of this paper is to apply the nonlinear superposition principle to some non-holonomic systems, in particular, those in chained and power forms, which are used to represent the kinematic equations of various non-holonomic wheeled vehicles. The existence of nonlinear superposition formulas is studied on the basis of Lie algebraic analysis. First, it is shown that nonlinear superposition formulas can be constructed using the knowledge of n + 1 particular solutions, using the affine structure of a system in chained form and the fact that a system in power form is diffeomorphic to a system in chained form. Secondly, using the notion of first integral, it is shown that only one particular solution is sufficient.