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Locus of a moving mass point

Two very small mass particles $m_1$, $m_2$ are connected by a $2l$ long, infinitely soft and inelastic thread without mass. The initial condition of the system before being freely released is as in ...
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Laws of physics for a point in cyclical 2D motion

A follow up question to the question in What does the statement "the laws of physics are invariant" mean? and Formal definition of an observer? Which laws of physics are they talking about ...