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Unformatted text preview: m moving in the presence of a spherically symmetric potential V ( r )= V ( r ). That is, L = 1 2 m r 2 + r 2 2 + r 2 sin 2 2 -V ( r ) . Identify as many conserved quantities ( i.e., constants of the motion) as you can from the mere structure of the Lagrangian. PROBLEM 4 Consider a point mass m on the surface of a sphere of radius R under the inuence of gravity-g z (spherical pendulum). 1. Write down the Lagrange function using spherical coordinates. 2. Find the Euler-Lagrange equations. 3. Calculate the special solutions for = constant . Describe this motion....
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- Spring '11