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Reflections on the "Saari Conjecture" and several new ones

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  • After explaining what motivated an earlier, yet unanswered conjecture whether a constant moment of inertia requires a relative equilibrium motion, several related conjectures follow and are described. One of them would generalize the $N$-body Virial Theorem. The mathematical obstacle hindering solution of all of these issues is identified and discussed.
    Mathematics Subject Classification: Primary: 70F10, 70F15; Secondary: 85A05.


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