@article{Owen2024, author = {Danny Owen and Nicola Baresi}, title = {Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits}, year = {2024}, journal = {Astrodynamics}, volume = {8}, number = {4}, pages = {577-595}, keywords = {circular restricted three-body problem (CR3BP), quasi-periodic torus, heteroclinic connection, knot theory}, url = {https://www.sciopen.com/article/10.1007/s42064-024-0201-0}, doi = {10.1007/s42064-024-0201-0}, abstract = {Heteroclinic connections represent unique opportunities for spacecraft to transfer between isoenergetic libration point orbits for zero deterministic 螖V expenditure. However, methods of detecting them can be limited, typically relying on human-in-the-loop or computationally intensive processes. In this paper we present a rapid and fully systematic method of detecting heteroclinic connections between quasi-periodic invariant tori by exploiting topological invariants found in knot theory. The approach is applied to the Earth鈥揗oon, Sun鈥揈arth, and Jupiter鈥揋anymede circular restricted three-body problems to demonstrate the robustness of this method in detecting heteroclinic connections between various quasi-periodic orbit families in restricted astrodynamical problems.} }