In Section 19.8 we used separation of variables to find a complete integral of the Hamilton–Jacobi..

In Section 19.8 we used separation of
variables to find a complete integral of the Hamilton–Jacobi equation for a
simple projectile.

(a) Use eqn (19.54) and the methods of Section
19.9 to write an F2 generating function for this system.

(b) Use this F2 generating function to
verify eqn (19.56), and also to find the evolution of the other variables x, y,
p0, px , py , pz as functions of q0 = t and the constant coordinates Qj and Pi
.