Continuity and Stability of families of figure eight orbits with finite angular momentum

Abstract

Numerical solutions are presented for a family of finite angular momentum orbits with three equal masses which connects the classical circular Lagrange orbit with the recently discovered planar figure eight orbit. Each member of this family is a periodic orbit in a frame rotating around the horizontal symmetry axis of the figure eight orbit. Numerical evidence is given that this family is a continuous function of the angular rotation frequency. Similar numerical solutions are also found for n>3 equal masses, where n is an odd integer. Finite angular momentum orbits also have been obtained for rotations along the two other symmetry axis of the figure eight orbit. The stability of these orbits is examined numerically without the restriction to a linear approximation.