The Hamiltonian Formalism for the Generalized Rigid Particles

The Hamiltonian formulation for the mechanical systems with reparametrization-invariant Lagrangians, depending on the worldline external curvatures is given, which is based on the use of moving frame. A complete sets of constraints are found for the Lagrangians with quadratic dependence on curvatures, for the lagrangians, proportional to an arbitrary curvature, and for the Lagrangians, linear on the first and second curvatures.