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Q72Section II (Mathematics)72 of 190

The momentum conjugate to a cyclic coordinate is conserved

The Lagrangian of a particle of mass mm in spherical polar co-ordinates is given by L=12m(r˙2+r2θ˙2+r2sin⁡2θ ϕ˙2)−mglcos⁡θL=\tfrac12m(\dot r^2+r^2\dot\theta^2+r^2\sin^2\theta\,\dot\phi^2) -mgl\cos\theta. The quantity that is conserved is:

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