The transformation of a 1D harmonic oscillator is given as:
For a one-dimensional system the canonicity of a transformation ((q,p)\rightarrow(Q,P)) is tested by evaluating the Poisson bracket ({Q,P}). A transformation is canonical if and ____ ______ ________ ______ _____ _____ _________ ________.
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The Lagrangian of a relativistic particle with charge e is given as:
Determine the Hamiltonian and the Hamilton's equation of motion:
The Lagrangian for a harmonic oscillator if given as:
The transformed coordinate under rotation about the Z-axis is given as:
Determine the corresponding y' so that the transformation leaves the Lagrangian invariant.
Derive the expression for total energy for a heavy symmetric top.
If , using Poisson bracket show that G generates a roation in X-Z plane.
The Hamiltonian of a system with two degrees of freedom is given as:
Determine the new Hamiltonian K.
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.