Nonlinear normal modes in a system with nonholonomic constraints

We investigate the dynamics of a system involving the planar motion of a ri gid body which is restrained by linear springs and which possesses a skate- like nonholonomic constraint known as Caplygin's sleigh. It is shown that t he system can be reduced to one with 2 1/2 degrees of freedom. The resultin g phase flow is shown to involve a curve of nonisolated equilibria. Using s econd-order averaging, the system is shown to possess two families of nonli near normal modes (NNMs). Each NNM involves two amplitude parameters. The s tructure of the NNMs is shown to depart from the generic form in the neighb orhood of a 1:1 internal resonance.