Homework Statement
Find the Linear momentum of an unwinding Cylinder with one end of a string attached to the ceiling. The mass of the cylinder is m and radius r. The cylinder is uniform and there is no slipping.
Homework Equations
Momentum, P = mv
moment of inertia , I = 1/2 MR^2...
I guess I did not phrase the question well.
The issue is I have a given hamiltonian H = 1/2(p1q2 + 2p1p2 + (q1)^2)
I need to solve this and I chose to begin by using the hamilton - jacobi equation and since we have no time dependence . If S is the hamilton action function then...
how would you solve the hamilton - jacobi equation for something with a hamiltonian with mixed terms like 1/2(p1q2 + 2p1p2 + (q1)^2)
well its quite trivial obtaining the HJ equation since there is no time dependence,
1/2( (ds/dq1)q2 + 2(ds/dq1)(ds/dq2) + (q1)^2 ) = E
I can't see how...