Hamiltonian formalism for particles with a generalized rigidity

The Hamiltonian formalism is developed for mechanical systems described by reparametrization-invariant Lagrangians dependent on the external curvatures of a world line. The complete sets of constraints are constructed for the Lagrangians quadratic in the external curvatures, the Lagrangians proportional to an arbitrary external curvature, and the Lagrangians linear in the first two curvatures.