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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2005, Volume 1, Number 1, Pages 143–154
(Mi nd194)
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This article is cited in 1 scientific paper (total in 1 paper)
A note by Poincaré
A. Chenciner ASD, IMCCE (UMR 8028 du CNRS), Observatoire de Paris,
Departement de Mathématiques,
Université D. Diderot
Abstract:
On November 30th 1896, Poincaré published a note entitled “On the periodic solutions and the least action principle” in the “Comptes rendus de l'Académie des Sciences”. He proposed to find periodic solutions of the planar Three-Body Problem by minimizing the Lagrangian action among loops in the configuration space which satisfy given constraints (the constraints amount to fixing their homology class). For the Newtonian potential, proportional to the inverse of the distance, the “collision problem” prevented him from realizing his program; hence he replaced it by a “strong force potential” proportional to the inverse of the squared distance.
In the lecture, the nature of the difficulties met by Poincaré is explained and it is shown how, one century later, these have been partially resolved for the Newtonian potential, leading to the discovery of new remarkable families of periodic solutions of the planar or spatial $n$-body problem.
Keywords:
Poincaré, three-body problem, action minimizing periodic solutions.
Citation:
A. Chenciner, “A note by Poincaré”, Nelin. Dinam., 1:1 (2005), 143–154
Linking options:
https://www.mathnet.ru/eng/nd194 https://www.mathnet.ru/eng/nd/v1/i1/p143
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Abstract page: | 364 | Full-text PDF : | 180 | First page: | 1 |
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