Quick Question in projectile motion (H-J)

[M. next]

In Hamilton Jacobi Equation (Projectile in two dimentions [x,y]), Isn't it correct that x is a cyclical coordinate?

 

[Simon Bridge]

You could figure that out by considering what "cyclical coordinate" means, then examining your Hamiltonian with this in mind. Of course, you can anticipate the answer from the way that a coordinate becomes non-cyclical.

The quick answer is: depends.