How do you solve hamilton jacobi equations of motion? - Answers

This method was governed by a variational principle applied to a certain function. The resulting variational relation was then treated by introducing some unknown multipliers in connection with constraint relations. After the elimination of these multipliers the generalized momenta were found to be certain functions of the partial derivatives of the Hamilton Jacobi function with respect to the generalized coordinates and the time. Then the partial differential equation of the classical Hamilton-Jacobi method was modified by inserting these functions for the generalized momenta in the Hamiltonian of the system.