Determine the Hamitonian and the value of so that the transformation is canonical.
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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.
A rigid body consisting of a uniform plate with and mass M, obtain the moments of inertia (Ixx, Iyy, Izz) and hence the principal moments of inertia.
Write down the expression for the Routhian for a bead of mass m sliding due to gravity on an elliptical wire for which the Lagrangian is given as:
Hence derive the equation of motion.
The Lagrangian of a relativistic particle with charge e is given as:
The Hamiltonian of a system with two degrees of freedom is given as:
Determine the new Hamiltonian K.
If , using Poisson bracket show that G generates a roation in X-Z plane.
Obtain the generating function F1(q, Q). Using F1(q, Q), obtain F2(q, P).