Obtain the radial action and the angular action variables. Hence, express the total action.
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The Hamiltonian of a system with two degrees of freedom is given as:
Determine the new Hamiltonian K.
Obtain the radial action and the angular action variables. Hence, express the total action.
Obtain the expression for the rotational kinetic energy of a rigid body when the rotation is referred to its principal axes of inertia, for a spherical top (a uniform solid sphere).
A simple pendulum with a bob of mass m and a string of length l0 with Hamiltonian
Construct Hamilton-Jacobi equation and obtain the characteristic function in integral form. Write the new coordinates P, Q.
The Lagrangian of a bead of m moving without friction along a wire bent in the shape of a parabola in the X-Y pane with is given by:
Obtain the generating function F1(q, Q). Using F1(q, Q), obtain F2(q, P).
Determine the Hamiltonian and the Hamilton's equation of motion: