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

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

Jun 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991arrma.115..153l&link_type=abstract

Archive for Rational Mechanics and Analysis, Volume 115, Issue 2, pp.153-165

Physics

2

Scientific paper

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 6 N×6 N 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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