(a) Verify that the general solution in eqn (19.78) satisfies the Hamilton–Jacobi equation eqn...

(a) Verify that the general solution in eqn
(19.78) satisfies the Hamilton–Jacobi equation eqn (19.66). (b) Verify that
this general solution contains the initial curve eqn (19.67).

(a) Following the pattern in Section 19.10,
carry out the details of the solution of the Cauchy problem for the
mono-energetic integral in Section 19.11. (b) Verify that the solution in eqns
(19.90, 19.91) satisfies the mono-energetic Hamilton– Jacobi equation eqn
(19.88) and contains the initial curve eqn (19.87).