Abstract. A geometric approach to the theory of non-holonomic systems is presented. General first order mechanical systems (not necessarily regular or Lagran\-gian) are studied. A constraint structure on $J^1Y$ is given by a submanifold fibered over $Y$, naturally endowed with a distribution (of a constant rank, possibly non-integrable). Constraint force is studied and geometric arguments for obtaining the Chetaev formula are presented. Constrained mechanical systems are geometrically described, their motion equations in intrinsic form are found, and dynamics are characterized by means of distributions on the constraint submanifold.
AMSclassification. 58F05, 70F25, 70H35
Keywords. Mechanical system, Lagrangian system, non-holonomic constraints, holonomic constraints, constraint distribution, Chetaev bundle, virtual displacements, constraint force, constrained equations of motion, regularity