Astronomy and Astrophysics – Astronomy
Scientific paper
Dec 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cemda..46..335k&link_type=abstract
Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 46, no. 4, 1989, p. 335-381.
Astronomy and Astrophysics
Astronomy
4
Euler-Lagrange Equation, Predictor-Corrector Methods, Three Body Problem, Differential Equations, Equations Of Motion
Scientific paper
The predictor-corrector method is described for numerically extending with respect to the parameters of the periodic solutions of a Lagrangian system, including recurrent solutions. The orbital stability in linear approximation is investigated simultaneously with its construction. The method is applied to the investigation of periodic motions, generated from Lagrangian solutions of the circular restricted three body problem. Small short-period motions are extended in the plane problem with respect to the parameters h, mu (h = energy constant, mu = mass ratio of the two dominant gravitators), small vertical oscillations are extended in the three-dimensional problem with respect to the parameters h, mu. For both problems in parameter's plane h, mu domains of existence and stability of derived periodic motions are constructed, resonance curves of third and fourth orders are distinguished.
Karimov S. R.
Sokol'Skii A. G.
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