Asymmetric periodic orbits in the photogravitational Copenhagen problem

摘要

In this paper we study the Ox-asymmetric solutions of the planar photogravitational restricted three-body problem in the case of primaries with equal masses and equal values of the radiation pressure parameters. In particular, we are concerned with the families of asymmetric orbits which bifurcate from the well known families a, b, and c. Their evolution is examined via the numerical construction of series of the critical bifurcation points of a, b, and c with respect to the variation of the common radiation parameter q. We also present some illustrative cases of these families for several values of this parameter. In order to avoid the singularity due to binary collisions between the third body and one of the primaries, the equations of motion of the problem are regularized by using the Levi-Civita transformations.