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Computational and Applied Mathematics Discussion Group
Jade Abbort
(University of Cape Town, )
Hi pips! Can someone help me with this question: A particle of mass m moves in R3 under a central force F(r) = −dV/dr , in spherical coordinates, so (x, y, z) = (r cos(φ) sin(θ), r sin(φ) sin(θ), r cos(θ)). Find the Lagrangian from first principles, in terms of (r, θ, φ) and their time derivatives. Hence (a) show that h, defined by h = mr2φ˙ sin2(θ) is a constant of the motion. (b) derive the other two equations of motion.
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