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Analytic-numerical solutions of restricted non-resonance planar three-body problem

Published online by Cambridge University Press:  25 May 2016

Y. A. Ryabov
Y. A. Ryabov*
Affiliation:
Moscow Automobile & Highway Engineering University Leningradsky pr.64, Moscow, 125829, Russia

Extract

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We consider a restricted planar circular three-body problem (Sun-Jupiter-asteroid) in a non-resonance case. There are two new algorithms developed for construction of a quasi-periodic solution in a trigonometric form by means of computer algebra. The first corresponds to classical method of simple iterations leading to series in powers of small mass mJ, the second, to iterations with rapid (quadratic) convergence, but having ordinary type and not involving a successive coordinate transformations. All these iterations require a realization of algebraic operations on trigonometric polynomials with the help of computers of high capacity. It would be interesting to compare the solutions obtained with the two algorithms and to estimate the domain of their practical convergence.

Type
Part VII - The Calculus of Perturbations
Information
Symposium - International Astronomical Union , Volume 172: Dynamics, Ephemerides and Astrometry of the Solar System , 1996 , pp. 289 - 292
Copyright
Copyright © Kluwer 1996 

References

Grebenikov, E., Ryabov, Y. Constructive methods in the analysis of nonlinear systems.-Moscow, ed.MIR, 1983, 324 p.Google Scholar