AAS 99-161

Three-Dimensional Periodic Solutions that Bifurcate from Halo Families in the Circular Restricted Three Body Problem

K.C. Howell, E.T. Campbell

Purdue University, West Lafayette, IN


The restricted problem of three bodies is of fundamental importance in mechanics, with significant applications to astrodynamics. During the last century, much effort has been focused on the search for periodic solutions since they are a key component in understanding the behavior in the non-integrable three-body problem. Numerous families of PLANAR periodic solutions have been computed and their relationships investigated. With vastly improved computational capabilities, THREE-DIMENSIONAL periodic families have appeared in recent years; halo orbits have, perhaps, been the most visible with their link to spacecraft mission design. Although an infinite number of three-dimensional periodic orbits exist, they are difficult to locate, as well as compute, and a random numerical search will never be successful. Thus, the study of bifurcations, where several families come together, is critical and used as the basis of the current study. In this effort, the L1 and L2 halo orbits serve as the baseline families; a number of bifurcations and intersections representing the existence of other three-dimensional families are identified. Various orbits are numerically computed as members of these intersecting families. A subset of these additional periodic orbits are examined for potential mission design applications.