The variational equation of the three-body problem

Details The variational equation of the three-body problem The variational equation of the three-body problem

Feb 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980cemec..21..171w&link_type=abstract

(Conference on Mathematical Methods in Celestial Mechanics, 6th, Oberwolfach, West Germany, Aug. 14-19, 1978.) Celestial Mechani

Mathematics

Equations Of Motion, Hypergeometric Functions, Three Body Problem, Celestial Mechanics, Differential Equations, Transformations (Mathematics)

Scientific paper

The variational equation of the three-body problem at a homothetic solution is considered. It is shown that this system of differential equations can be solved exactly in terms of hypergeometric functions by using the scaled true anomaly of the one-dimensional Kepler motion as the independent variable. The immediate neighborhood of a homothetic solution can thus be described quantitatively, at least in a linearized approximation which is only valid in an open time interval between two collisions of the reference solution.

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