Symmetries of mechanical systems with nonlinear nonholonomic constraints

The dynamical symmetries and adjoint symmetries of nonlinear nonholonomic c onstrained mechanical systems are analysed in two kinds of geometrical fram eworks whose evolution equations are Routh's equations and generalized Chap lygin's equations, respectively. The Lagrangian inverse problem and the int errelation between Noether's symmetries and dynamical symmetries are briefl y concerned with. Finally an illustrative example is analysed.