Three-Body Problem with Variable Masses that Change Anisotropically at Different Rates
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Abstract
In this paper we consider a general case of the three-body problem with variable masses that change anisotropically at different rates. Due to the change of masses reactive forces appear which significantly complicate the problem. Equations of motion of the system have been derived in Jacobi coordinates for the first time. Using these equations of motion and applying the methods of perturbation theory in modified Jacobi and Delaunay elements, we have obtained canonical equations of perturbed motion of the system in the presence of reactive forces. Canonical system of equations for secular perturbations in the three-body problem with variable masses changing anisotropically was derived in explicit form in terms of the analogues of the second system of Poincaré elements. An approximate analytical solution of the differential equations for secular perturbations was obtained by Picard’s method.
Keywords
Three-body problem Variable masses Reactive forces Secular perturbations Analogues of the Poincare second systemMathematics Subject Classification
Primary 70F07 Secondary 70P05Preview
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