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:
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A particle of mass m moves under a potential . The total energy of the system is
where l is the angular momentum.
The Lagrangian of a relativistic particle with charge e is given as:
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.
Determine the Hamitonian and the value of so that the transformation is canonical.
Obtain the generating function F1(q, Q). Using F1(q, Q), obtain F2(q, P).
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).