Elimination of the nodes in problems of N bodies

Details Elimination of the nodes in problems of N bodies Elimination of the nodes in problems of N bodies

Jun 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..30..181d&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 30, June 1983, p. 181-195.

Mathematics

7

Angular Momentum, Many Body Problem, Mathieu Function, Perturbation Theory, Canonical Forms, Kinetic Equations, Quaternions, Transformations (Mathematics)

Scientific paper

In application of the Reduction Theorem to the general problem of n (equal to or greater than three) bodies, a Mathieu canonical transformation is proposed whereby the new variables separate naturally into (1) a coordinate system on any reduced manifold of constant angular momentum, and (2) a quadruple made of a pair of ignorable longitudes together with their conjugate momenta. The reduction is built from a binary tree of kinetic frames. Explicit transformation formulas are obtained by induction from the top of the tree down to its root at the invariable frame; they are based on the unit quaternions which represent the finite rotations mapping one vector base onto another in the chain of kinetic frames. The development scheme lends itself to automatic processing by computer in a functional language.

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