Abstract:Consider the planar Newtonian (2N + 1)-body problem, N ≥ 1, with 2N bodies of unit mass and one body of mass m. Using the discrete symmetry due to the equal masses and reducing by the rotational symmetry, we show that solutions with the 2N unit mass points at the vertices of two concentric regular N -gons and m at the centre at all times form invariant manifold. We study the regular 2N -gon with central mass m relative equilibria within the dynamics on the invariant manifold described above. As m varies, we id… Show more
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