A unified geometric approach to nonholonomic constrained mechanical systems is applied to several concrete problems from the classical mechanics of particles and rigid bodies. In every of these examples the given constraint conditions are analysed, a corresponding constraint submanifold in the phase space is considered, the corresponding constrained mechanical system is modelled on the constraint submanifold, the reduced equations of motion of this system (i.e. equations of motion defined on the...

Given a Lagrangian system with non-holonomic constraints we construct an almost product structure on the tangent bundle of the configuration manifold such that the projection of the Euler-Lagrange vector field gives the dynamics of the system. In a degenerate case, we develop a constraint algorithm which determines a final constraint submanifold where a completely consistent dynamics of the initial system exists.

In this paper we derive general equations for constraint Noethertype symmetries of a first order non-holonomic mechanical system and the corresponding currents, i.e. functions constant along trajectories of the nonholonomic system. The approach is based on a consistent and effective geometrical theory of nonholonomic constrained systems on fibred manifolds and their jet prolongations, first presented and developed by Olga Rossi. As a representative example of application of the geometrical theory...