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- W2592413541 abstract "We use numerical continuation and bifurcation techniques in a boundary value setting to follow Lyapunov families of periodic orbits and subsequently bifurcating families. The Lyapunov families arise from the polygonal equilibrium of n bodies in a rotating frame of reference. When the frequency of a Lyapunov orbit and the frequency of the rotating frame have a rational relationship, then the orbit is also periodic in the inertial frame. We prove that a dense set of Lyapunov orbits, with frequencies satisfying a diophantine equation, correspond to choreographies. We present a sample of the many choreographies that we have determined numerically along the Lyapunov families and along bifurcating families, namely for the cases $$n=3$$ , 4, and 6–9. We also present numerical results for the case where there is a central body that affects the choreography, but that does not participate in it. Animations of the families and the choreographies can be seen at the link below." @default.
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- W2592413541 date "2018-07-01" @default.
- W2592413541 modified "2023-10-16" @default.
- W2592413541 title "Symmetries and choreographies in families that bifurcate from the polygonal relative equilibrium of the n-body problem" @default.
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- W2592413541 doi "https://doi.org/10.1007/s10569-018-9841-9" @default.
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