A dynamical formalism of singular Lagrangian system with higher derivatives

Abstract

The singular Lagrangian system with higher derivatives is analyzed with the aid of the Ostrogradski transformation and the Dirac formalism. The formulation of canonical theory is developed so that the equivalence between the Lagrange formalism and the Hamilton one is maintained. As a practical example, the acceleration-dependent potentials appearing in the Lagrangian of two-point particles interacting gravitationally are dealt with and the equivalence between the two Hamiltonians that follow from the two Lagrangians which are related by the coordinate transformations is shown. It is also shown, when the constraints are all first class, that a consistent generator of gauge transformation is constructed. Typical examples are given.