New phenomenons in the spatial isosceles three-body problem

Abstract

In this work, we study the periodic orbits in the spatial isosceles three-body problem. These periodic orbits form a one-parameter set with a rotation angle $\theta$ as the parameter. Some new phenomenons are discovered by applying our numerical method. The periodic orbit coincides with the planar Euler orbit when $0<\theta \le 0.32\pi$ and it changes to a spatial orbit when $0.33\pi \le \theta <\pi$. Eventually, the spatial orbit becomes a planar collision orbit when $\theta =\pi$. Furthermore, an oscillated behavior is found when $\theta =\pi /2$, which is chaotic but bounded under a small perturbation. As another application of our numerical method, 7 new periodic orbits are presented in the end.

References in corpus (3)

• Three Classes of Newtonian Three-Body Planar Periodic Orbits
• Probing the local dynamics of periodic orbits by the generalized alignment index (GALI) method
• Interplay Between Chaotic and Regular Motion in a Time-Dependent Barred Galaxy Model