Elimination of nodes in the Newtonian four-body problem

Details Elimination of nodes in the Newtonian four-body problem Elimination of nodes in the Newtonian four-body problem

Aug 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..27..399b&link_type=abstract

Celestial Mechanics, vol. 27, Aug. 1982, p. 399-414. In French.

Physics

2

Canonical Forms, Celestial Mechanics, Four Body Problem, Hamilton-Jacobi Equation, Angular Momentum, Center Of Gravity, Nonrelativistic Mechanics, Numerical Stability

Scientific paper

The method of canonical transformations with imposed variables is applied to the reduction of the Newtonian four-body problem. The problem is reduced to that of three fictitious bodies by eliminating the center of gravity, and the actual reduction is done by using the integrals of angular momentum in Hamiltonian formulation and considering the geometrical aspects of the elimination of the nodes advanced by Jacobi. Three functions are imposed as new variables, the third integral of angular momentum and two invariant functions. The last two remain null when the axis, defined by the momentum vector of the four bodies, is taken as the third coordinate axis; they are chosen in involution with the third integral of momentum so that their Poisson bracket equals one. A system of fourteen canonical variables is determined which has a simple geometrical interpretation.

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