Hip-hop solutions of the 2N-body problem
Hip-hop solutions of the 2N-body problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2N-gon relative equilibria with small vertical oscillations. For fixed N, an infinity of these solutions are three-dimensional choreographies, with all the bodies moving along the same closed curve in the inertial frame.
KeywordsN-body problem Analytic continuation Hip-hop Choreographies
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- Chenciner, A.: Action minimizing solutions of the newtonian n-body problem: from homology to symmetry. In: Proceedings of the International Congress of Mathematicians, vol. III, Beijing, pp. 279–294 (2002) (Errata. Proceedings of the International Congress of Mathematicians) (Beijing, 2002) Vol. 1, 651–653MathSciNetGoogle Scholar
- Chenciner, A., Gerver, J., Montgomery, R., Simó, C.: Simple Choreographic Motions of N Bodies: A Preliminary Study, Geometry, Mechanics, and Dynamics, pp. 287–308. Springer, New York (2002)Google Scholar
- Meyer, K.R., Hall, G.R.: Introduction to Hamiltonian Dynamical Systems and the N-body Problem, Vol. 90 of Applied Mathematical Sciences. Springer-Verlag, New York (1992)Google Scholar
- Simó, C.: New families of solutions in N-body problems. In: Proceedings of the third European Congress of Mathematics, in Prog. Math. 201, 101–115 (2001)Google Scholar
- Terracini, S., Venturelli, A.: Symmetric trajectories for the 2n-body problem with equal masses (2005) preprintGoogle Scholar