Determine the Hamiltonian and the Hamilton's equation of motion:
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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:
The Lagrangian of a relativistic particle with charge e is given as:
Derive the expression for total energy for a heavy symmetric top.
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).
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.