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Kashmir
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Done.vanhees71 said:
A Cyclic coordinates in a two body central force problem
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The discussion centers on the implications of spherical symmetry in the context of conservative central forces and the Lagrangian formulation of mechanics. It highlights that while the angle coordinate ##\phi## is cyclic, allowing for the conservation of angular momentum, the coordinate ##\theta## is not cyclic due to its presence in the Lagrangian. This distinction leads to the conclusion that only one component of angular momentum is explicitly conserved along the chosen polar axis, despite the overall conservation of angular momentum in three dimensions. The conversation also touches on the historical context of physics textbooks and the challenges faced by authors in conveying complex concepts. Ultimately, the participants seek clarity on the relationship between cyclic coordinates and conservation laws in mechanics.