Bm. Pimentel et Rg. Teixera, HAMILTON-JACOBI FORMULATION FOR SINGULAR SYSTEMS WITH 2ND-ORDER LAGRANGIANS, Nuovo cimento della Societa italiana di fisica. B, Relativity, classical and statistical physics, 111(7), 1996, pp. 841-854
Recently, the Hamilton-Jacobi formulation for first-order constrained
systems has been developed. In such formalism the equations of motion
are written as total differential equations in many variables. We gene
ralize the Hamilton-Jacobi formulation for singular systems with secon
d-order Lagrangians and apply this new formulation to Podolsky electro
dynamics, comparing with the results obtained through Dirac's method.