Computer algebra and the elliptic restricted problem of three bodies (original) (raw)

Abstract

Perturbation solutions of differential equations typically involve power series expansions in a small parameter. Computer algebra has proven to be a useful tool for the treatment of perturbation problems due to the large quantities of algebra involved. As an example, a problem which was previously handled both by numerical integration and by hand-derived perturbation analysis is treated by computer algebra. The elliptic restricted problem of three bodies describing the planar motion of a particle (the third body) under the gravitational attraction of two masses (the primaries) which move about their common center of mass in elliptical orbits is examined. Specifically, the stability of the L(sub 4) equilibrium, located at the vertex of an equilateral triangle which is positioned so that the primaries lie at the other two vertices is determined. It is shown that the use of computer algebra yields a vast increase in the number of terms obtained in the perturbation expansion, and raises...

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