A geometrical framework for the study of non-holonomic Lagrangian systems

A geometrical framework is presented for the treatment of a class of dynamical systems, which are modelled by a system of second-order differential equations, coupled with first-order equations linear in the derivatives. Such problems in particular make their appearance in the study of Lagrangian systems with non-holonomic constraints. Among other things, we discuss the concepts of symmetry and adjoint symmetry for such systems and identify for that purpose an appropriate notion of 'dynamical covariant derivative' and 'Jacobi endomorphism'. The intrinsic tools which are being developed further allow a direct geometrical construction of the dynamics of non-holonomic systems. The vertically rolling disc is chosen as an illustrative example for the newly proposed formalism and results.