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Binary trees, symplectic matrices and the Jacobi coordinates of celestial mechanics

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Abstract

A graph-theoretic algorithm for constructing the Jacobi coordinates in celestial mechanics is given. To every full binary tree with N leaves, there corresponds a 6N×6N symplectic matrix, which defines a Jacobi transformation. This correspondence yields a direct proof of the symplectic property for all the Jacobi coordinates; hitherto, only special examples of these transformations have been shown to be canonical.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 12180, Troy, New York

    Chjan C. Lim

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  1. Chjan C. Lim
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Communicated by R. P. McGeehee

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Lim, C.C. Binary trees, symplectic matrices and the Jacobi coordinates of celestial mechanics. Arch. Rational Mech. Anal. 115, 153–165 (1991). https://doi.org/10.1007/BF00375224

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  • DOI: https://doi.org/10.1007/BF00375224

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