The Geometry of Non-Holonomic Lagrangian systems

D. J. Saunders


Abstract. A non-holonomic Lagrangian system may often be represented by an unconstrained system and a submanifold of a jet space (the constraint submanifold). We look here at the ways in which such a representation may arise, the conditions describing the regularity of such a system, and the different ways in which Hamiltonian representations may be obtained. We find that regularity of the unconstrained system is not a prerequisite for regularity of the constrained system. If the constraints have been derived from a connection then two different Hamiltonian representations may be obtained; for non-linear constraints, these give rise to two different regularity conditions.

AMSclassification. 58F05 (70G50)

Keywords. Non-holonomic, Lagrangian