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Unformatted text preview: (18) Consider the spherical pendulum of mass m again. (a) Use the Legendre transformation H ( , , p , p ) = p + p -L ( , , , ) , to construct the Hamiltonian of the system and show that it is identical to the energy E = T + V . (b) Write down Hamiltons equations of motions for the system and identify a conserved quantity. Due February 3 before class (6 points). (19) Calculate explicitly x i L ( i = 1 , . . . , 3) for the Lagrangian of the 3D Kepler problem L = m 1 2 ( ~x 1 ) 2 + m 2 2 ( ~x 2 ) 2-g m 1 m 2 | ~x 1-~x 2 | Are there associated conservation laws? Due February 3 in class (4 points)....
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This note was uploaded on 11/10/2011 for the course PHY 4241 taught by Professor Berg during the Spring '11 term at University of Florida.
- Spring '11