Maupertuis's principle for systems with Lagrangians linear in velocities

Maupertuis's variational principle is discussed for Lagrangian systems with Lagrangian which is linear in generalized velocities. In particular, this includes Hamiltonian systems in the Poincaré-Helmholtz representation. Our approach allows us to indicate a new variational principle for systems whose Lagrangians are degenerate in velocities. In its derivation we use Dirac's generalized Hamiltonian formalism. Bibliography: 15 titles.