1. The problem statement, all variables and given/known data a) the lagrangian for a system of one degree of freedom can be written as. L= (m/2) (dq/dt)2sin2(wt) +q(dq/dt)sin(2wt) +(qw)2 what is the hamiltonian? is it conserved? b) introduce a new coordinate defined by Q = qsin(wt) find the lagrangian and hamiltonian with the new coordinate and is it conserved? 2. Relevant equations qp-L = H 3. The attempt at a solution Just wondering what the method is to solve b) or is it as simple as q = Q/sin(wt) (dq/dt) = (dQ/dt)/sin(wt) - Qwcos(wt)/(sin2(wt)) subbing that in and solving? I'm assuming that this change of coordinate is supposed to make the Hamiltonian independent of time and therefore conserved. Yet what i found is not conserved, so i assume i used the wrong method.