(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.
(a) show that h, defined by h = mr2φ˙ sin2(θ) is a constant of the motion.
(b) derive the other two equations of motion.
September 23 2020, 1:39 am