2. Integrate the equations of motion for a spherical pendulum, i.e., a particle of mass m moving on the surface of a sphere of radius / in a gravitational field, with Lagrangian L= ml² -(0² + psin² 0) +mglcos 0. 2 Hint: Merely set up the integrals, do not evaluate them. You should obtain two integrals w.r.t. de: one determining t and another determining p. Express the first integral in terms of E,Ueff, m, and l. Express the second integral in terms of E,Ueff, m, l, and M₂.
2. Integrate the equations of motion for a spherical pendulum, i.e., a particle of mass m moving on the surface of a sphere of radius / in a gravitational field, with Lagrangian L= ml² -(0² + psin² 0) +mglcos 0. 2 Hint: Merely set up the integrals, do not evaluate them. You should obtain two integrals w.r.t. de: one determining t and another determining p. Express the first integral in terms of E,Ueff, m, and l. Express the second integral in terms of E,Ueff, m, l, and M₂.
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Transcribed Image Text:2. Integrate the equations of motion for a spherical pendulum, i.e., a particle of mass m
moving on the surface of a sphere of radius / in a gravitational field, with Lagrangian
L =
ml²
-(0² + psin² 0) + mglcos 0.
2
Hint: Merely set up the integrals, do not evaluate them. You should obtain two integrals
w.r.t. de: one determining t and another determining p. Express the first integral in terms of
E,Ueff, m, and l. Express the second integral in terms of E,U eff, m, l, and M₂.
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