Abstract:Hip-Hop solutions of the 2N -body problem are solutions that satisfy at every instance of time, that the 2N bodies with the same mass m, are at the vertices of two regular N -gons, each one of these N -gons are at planes that are equidistant from a fixed plane Π0 forming an antiprism. In this paper, we first prove that for every N and every m there exists a family of periodic hip-hop solutions. For every solution in these families the oriented distance to the plane Π0, which we call d(t), is an odd function th… Show more
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