A dynamical formalism of singular Lagrangian system with higher derivatives

Yoshihiko Saito and Reiji Sugano
Department of Physics, Osaka City University, Osaka 558, Japan
Tadayuki Ohta
Department of Physics, Miyagi University of Education, Sendai 980, Japan
Toshiei Kimura
Research Institute of Theoretical Physics, Hiroshima University, Takehara, Hiroshima 725, Japan

(Received 11 March 1988; accepted 11 January 1989)

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.