Since the discovery of the figure-eight orbit for the three-body problem [Moore, C., 1993, Phys. Rev. Lett., 70, pp. 3675–3679] a large number of periodic orbits of the -body problem with equal masses and beautiful symmetries have been discovered. However, most of those that have appeared in the literature are either planar or are obtained from perturbations of planar orbits. Here we exhibit a number of new three-dimensional periodic -body orbits with equal masses and cubic symmetry, including some whose moment of inertia tensor is a scalar. We found these orbits numerically, by minimizing the action as a function of the trajectories’ Fourier coefficients. We also give numerical evidence that a planar three-body orbit first found in [Hénon, M., 1976, Celest. Mech., 13, pp. 267–285], rediscovered by [Moore, 1993], and found to exist for different masses by [Nauenberg, M., 2001, Phys. Lett., 292, pp. 93–99], is dynamically stable.
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October 2006
Research Papers
New Periodic Orbits for the -Body Problem
Cristopher Moore,
Cristopher Moore
Computer Science Department, and Department of Physics and Astronomy,
University of New Mexico
, Albuquerque, NM 87501 and the Santa Fe Institute
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Michael Nauenberg
Michael Nauenberg
Physics Department,
University of California, Santa Cruz
, Santa Cruz, CA
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Cristopher Moore
Computer Science Department, and Department of Physics and Astronomy,
University of New Mexico
, Albuquerque, NM 87501 and the Santa Fe Institute
Michael Nauenberg
Physics Department,
University of California, Santa Cruz
, Santa Cruz, CAJ. Comput. Nonlinear Dynam. Oct 2006, 1(4): 307-311 (5 pages)
Published Online: March 15, 2006
Article history
Received:
November 8, 2005
Revised:
March 15, 2006
Citation
Moore, C., and Nauenberg, M. (March 15, 2006). "New Periodic Orbits for the -Body Problem." ASME. J. Comput. Nonlinear Dynam. October 2006; 1(4): 307–311. https://doi.org/10.1115/1.2338323
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