Unformatted text preview: (18) Consider the spherical pendulum of mass m again. (a) Use the Legendre transformation H ( θ, φ, p θ , p φ ) = ˙ θp θ + ˙ φp φL ( θ, φ, ˙ θ, ˙ φ ) , to construct the Hamiltonian of the system and show that it is identical to the energy E = T + V . (b) Write down Hamilton’s equations of motions for the system and identify a conserved quantity. Due February 3 before class (6 points). (19) Calculate explicitly δ 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 ) 2g m 1 m 2  ~x 1~x 2  Are there associated conservation laws? Due February 3 in class (4 points)....
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 Spring '11
 Berg
 Work, Fundamental physics concepts, Hamiltonian mechanics, Noether's theorem, conservation law, harmonically bound particles

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