BIFURCATIONS OF PLANE WITH 3-DIMENSIONAL ASYMMETRIC PERIODIC ORBITS IN RESTRICTED 3-BODY PROBLEM

The aim of this paper is the detection of three-dimensional asymmetric periodic orbits. An iterative procedure is described for the determination of the bifurcations of families of plane asymmetric periodic solutions of the restricted three-body problem with such of three-dimensional ones. It is applied to the two previously established bifurcations of this type. For each of them a 'bifurcation series' is obtained covering the entire range of the mass parameter of the problem. The stability of these bifurcation orbits is examined and it is found that in each case there are two subintervals of the range of the mass parameter for which these orbits are stable, one of them containing cases of astronomical interest. Typical three-dimensional asymmetric periodic orbits of the bifurcating families are also given. © 1977 Royal Astronomical Society.