A numerical scheme to obtain periodic three-body orbits with finite angular momentum

The three-body problem is ubiquitous in various physical systems. Thousands of periodic orbits for the three-body problem with zero angular momentum were obtained in recent years. In this paper, we present a numerical scheme to obtain periodic orbits for the three-body problem with finite angular momentum. The proposed approach combines a continuation method and the Newton–Raphson method, which are implemented using Clean Numerical Simulation (CNS) for the integration of the equations of motion. The figure-eight periodic orbit and another newly found periodic orbit are taken to generate periodic orbits by continuously varying the angular momentum. The linear stability of these periodic orbits are investigated through Floquet theory. It is suggested that angular momentum plays a significant role in influencing the linear instability of periodic orbits. Our proposed numerical approach inspires the further research in the intricate dependence of the periodic orbits on the angular momentum, providing a powerful tool for investigating the nonlinear dynamics of the three-body problem.