Linear stability for some symmetric periodic simultaneous binary collision orbits in the four-body problem

作者：Bakker Lennard F^*; Ouyang Tiancheng; Yan Duokui; Simmons Skyler; Roberts Gareth E

来源：Celestial Mechanics and Dynamical Astronomy, 2010, 108(2): 147-164.

DOI：10.1007/s10569-010-9298-y

• N-body problem
• Singular periodic orbits
• Stability
• Schubart-like orbit
• Roberts' method

We apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four-body problem with masses 1, m, m, 1, and also in a symmetric planar four-body problem with equal masses. In both problems, the assumed symmetries reduce the determination of linear stability to the numerical computation of a single real number. For the collinear problem, this verifies the earlier numerical results of Sweatman for linear stability with respect to collinear and symmetric perturbations.

• 出版日期2010-10
• 单位南开大学