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- W2950235918 abstract "In his fondamental Essay on the 3-body problem, Lagrange, well before Jacobi's of the node, carries out the first complete reduction of symetries. Discovering the so-called homographic motions, he shows that they necessarily take place in a fixed plane. The true nature of this reduction is revealed if one considers the n-body problem in an euclidean space of arbitrary dimension. The actual dimension of the ambiant space then appears as a constraint, namely the angular momentum bivector's degeneracy. The main part of this survey is a detailed description of the results obtained in a joint paper with Alain Albouy published in french (Inventiones 1998): for a non homothetic homographic motion to exist, it is necessary that the space of motion be even dimensional. Two cases are possible: either the configuration is central (that is a critical point of the potential among configurations with a given moment of inertia) and the space where the motion takes place is endowed with an hermitian structure, or it is balanced (that is a critical point of the potential among configurations with a given inertia spectrum) and the motion is a new type, quasi-periodic, of relative equilibrium. Hip-Hops, which are substitutes to the non-existing homographic solutions with odd dimensional space of motion, are also discussed." @default.
- W2950235918 created "2019-06-27" @default.
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- W2950235918 date "2011-11-05" @default.
- W2950235918 modified "2023-09-27" @default.
- W2950235918 title "The Lagrange reduction of the N-body problem, a survey" @default.
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