1. The problem statement, all variables and given/known data Consider the transformation from the variables (q,p) to (Q,P) by virtue of q = q(Q,P), p = p(Q,P) and H(q,p,t) = H(Q,P,t). Show that the equations of motion for Q,P are: [itex]\partial[/itex]H/[itex]\partial[/itex]Q = -JDdP/dt [itex]\partial[/itex]H/[itex]\partial[/itex]P = JDdQ/dt where JD is the Jacobian determinant det([itex]\partial[/itex](q,p)/[itex]\partial[/itex](Q,P)) this shows the transformation is canonical only if JD=1. 2. Relevant equations 3. The attempt at a solution I have tried to write some equations which might help me. They can be found on the attached picture. I would like to know which these can get me on track of the solution. Also I would like to know if my expression for the Jaciobian determinant is correct. As a side question I would like to know why you can assume the two variables to have same hamiltonian. Is this because the transformation is not time dependent?