Addendum to a dynamical formalism of singular Lagrangian system with higher derivatives

Yoshihiko Saito

Osaka Museum of Science, Osaka 530, Japan

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

Hiroshima Prefectural University, Shobara-shi, Hiroshima 727, Japan

(Received 22 April 1991; accepted 28 September 1992)

A formulation for singular Lagrangians with higher derivatives in a previous paper is supplemented and a complete formulation of canonical theory for the systems is presented. It is shown that our previous formulation reproduces all constraints included in the Ostrogradski transformations, by using stationarity conditions of primary constraints. Secondarily, on the effect of adding a total time derivative term to a nonsingular Lagrangian with higher derivatives, the previous paper is revised so as to give a correct formulation for counting the numbers of first and second class constraints. It is concluded that the main part of our previous formulation needs no essential change.