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Advances in Astronomy
Volume 2015, Article ID 473483, 21 pages
Research Article

Equilibrium Points and Related Periodic Motions in the Restricted Three-Body Problem with Angular Velocity and Radiation Effects

1Department of Electrical & Computer Engineering, University of Patras, 26500 Patras, Greece
2Department of Civil Engineering, University of Patras, 26500 Patras, Greece
3Department of Computer Engineering & Informatics, University of Patras, 26500 Patras, Greece

Received 24 April 2015; Accepted 2 June 2015

Academic Editor: Zdzislaw E. Musielak

Copyright © 2015 E. A. Perdios et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper deals with a modification of the restricted three-body problem in which the angular velocity variation is considered in the case where the primaries are sources of radiation. In particular, the existence and stability of its equilibrium points in the plane of motion of the primaries are studied. We find that this problem admits the well-known five planar equilibria of the classical problem with the difference that the corresponding collinear points may be stable depending on the parameters of the problem. For all planar equilibria, sufficient parametric conditions for their stability have been established which are used for the numerical determination of the stability regions in various parametric planes. Also, for certain values of the parameters of the problem for which the equilibrium points are stable, the short and long period families have been computed. To do so, semianalytical expressions have been found for the determination of appropriate initial conditions. Special attention has been given to the continuation of the long period family, in the case of the classical restricted three-body problem, where we show numerically that periodic orbits of the short period family, which are bifurcation points with the long period family, are connected through the characteristic curve of the long period family.