We prove the existence of a new branch of solutions of Mountain Pass type for the periodic 3-body problem with choreographical constraint. At first we describe the variational structure of the action functional associated to the choreographical three body problem in R-3. In the second part, using a bisection algorithm, we provide a numerical non-rigorous solution of Mountain Pass type for this problem in a rotating frame with angular velocity 1.5. The last step consists in the rigorous computer-assisted proof of the existence of a full branch of solutions for the problem starting from the Mountain Pass solution detected numerically.
Arioli, G., Barutello, V., Terracini, S. (2006). A new branch of mountain pass solutions for the choreographical 3-body problem. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 268(2), 439-463 [10.1007/s00220-006-0111-4].
A new branch of mountain pass solutions for the choreographical 3-body problem
TERRACINI, SUSANNA
2006
Abstract
We prove the existence of a new branch of solutions of Mountain Pass type for the periodic 3-body problem with choreographical constraint. At first we describe the variational structure of the action functional associated to the choreographical three body problem in R-3. In the second part, using a bisection algorithm, we provide a numerical non-rigorous solution of Mountain Pass type for this problem in a rotating frame with angular velocity 1.5. The last step consists in the rigorous computer-assisted proof of the existence of a full branch of solutions for the problem starting from the Mountain Pass solution detected numerically.
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