Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976a%26a....51..117s&link_type=abstract
Astronomy and Astrophysics, vol. 51, no. 1, Aug. 1976, p. 117-126. In French.
Astronomy and Astrophysics
Astrophysics
8
Natural Satellites, Orbit Calculation, Periodic Functions, Perturbation Theory, Three Body Problem, Cartesian Coordinates, Circular Orbits, Equations Of Motion, Hill Lunar Theory, Lagrangian Equilibrium Points, Motion Stability, Orbit Perturbation
Scientific paper
The paper investigates the problem of the existence of periodic solutions in the restricted circular three-body problem for a system subjected to a periodic perturbation, when the unperturbed system has one or several periodic solutions depending on a certain number of parameters. Application of Haag's synchronization theory allows the determination of the existence and properties of solutions of the first kind in the sense of Poincare. A method is shown for constructing in Cartesian coordinates the solutions of the first kind with period equal to a whole-number multiple of the period of the perturbation function. Hill's periodic orbit in lunar theory is constructed in a Cartesian coordinate system.
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