Polygonal homographic orbits in spaces of constant curvature

Abstract

We prove that the geometry of the 2-dimensional $n$-body problem for spaces of constant curvature $\kappa \ne 0$, $n\ge 3$, does not allow for polygonal homographic solutions, provided that the corresponding orbits are irregular polygons of non-constant size.

References in corpus (1)

• Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere $S^2$ and the hyperbolic plane $H^2$