Abstract
Beyond the casen=3 little was known about relative equilibrium solutions of then-body problem up to recent years. Palmore's work provides in the general case much useful information. In the casen=4 he gives the totality of solutions when the four masses are equal and studies some degeneracies. We present here a survey of solutions for arbitrary masses, discussing the manifolds of degeneracy. The ordering of restricted potentials allows a counting of the number of bifurcation sets and different invariant manifolds. An analysis of linear stability is done in the restricted and general cases. As a result, values of the masses ensuring linear stability are given.
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Simó, C. Relative equilibrium solutions in the four body problem. Celestial Mechanics 18, 165–184 (1978). https://doi.org/10.1007/BF01228714
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DOI: https://doi.org/10.1007/BF01228714