equa 2. In the text, the Hamilton-Jacobi equation for S was obtained by seeking a con- tact transformation from the canonical coordinates (q. p) to the constants (a, 8). Conversely, if S(qi.a. t) is any complete solution of the Hamilton-Jacobi tion (10.3), show that the set of variables (Qi. Pi) defined by Eqs. (10.7) and (10.8) are canonical variables, that is, that they satisfy Hamilton's equations.