Computing Invariant Manifolds and Connecting Orbits in the Circular Restricted Three Body Problem
For researchers in astrodynamics and space-mission design, this provides a computational method to find connecting orbits in the CR3BP, though the approach is incremental.
The paper demonstrates the effectiveness of boundary value formulations with numerical continuation for computing stable and unstable manifolds in the Circular Restricted Three-Body Problem, detecting heteroclinic and homoclinic connections among periodic orbits and invariant tori, which may be useful for space-mission design.
We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable manifolds in systems of ordinary differential equations. Specifically, we consider the Circular Restricted Three-Body Problem (CR3BP), which models the motion of a satellite in an Earth- Moon-like system. The CR3BP has many well-known families of periodic orbits, such as the planar Lyapunov orbits and the non-planar Vertical and Halo orbits. We compute the unstable manifolds of selected Vertical and Halo orbits, which in several cases leads to the detection of heteroclinic connections from such a periodic orbit to invariant tori. Subsequent continuation of these connecting orbits with a suitable end point condition and allowing the energy level to vary, leads to the further detection of apparent homoclinic connections from the base periodic orbit to itself, or the detection of heteroclinic connections from the base periodic orbit to other periodic orbits. Some of these connecting orbits could be of potential interest in space-mission design.