1.I.9A
The action for a system with generalized coordinates for a time interval is given by
where is the Lagrangian. The end point values and are fixed.
Derive Lagrange's equations from the principle of least action by considering the variation of for all possible paths.
Define the momentum conjugate to . Derive a condition for to be a constant of the motion.
A symmetric top moves under the action of a potential . The Lagrangian is given by
where the generalized coordinates are the Euler angles and the principal moments of inertia are and .
Show that is a constant of the motion and give expressions for two others. Show further that it is possible for the top to move with both and constant provided these satisfy the condition
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