Classical Mechanics (Kibble & Berkshire) · Problem 12.20

The calculus of variations and Hamilton's principle — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · lagrangian-mechanics-symmetry-conservation

Problem

A particle moves freely in the gravitational field of a fixed mass distribution. Find the conservation principles that correspond to the symmetries of the following fixed mass distributions: (i) a uniform sphere, (ii) a uniform half plane, (iii) two particles, (iv) a uniform right circular cone, (v) an infinite uniform circular cylinder.

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