Danny Owen
About
My research project
Continuation of Heteroclinic Connections between Quasi-periodic OrbitsHeteroclinic connections between quasi-periodic orbits provide incredibly useful opportunities for novel spacecraft mission design. However, finding these connections is difficult. My research explores systematic methods of discovering these connections via dimension reduction methods. Once connections are found this way, we propose that pseudo-arc length continuation can be used to explore families of heteroclinic connections, removing much of the difficulty associated with exploiting these unique and useful trajectories.
Supervisors
Heteroclinic connections between quasi-periodic orbits provide incredibly useful opportunities for novel spacecraft mission design. However, finding these connections is difficult. My research explores systematic methods of discovering these connections via dimension reduction methods. Once connections are found this way, we propose that pseudo-arc length continuation can be used to explore families of heteroclinic connections, removing much of the difficulty associated with exploiting these unique and useful trajectories.
Publications
Methods of generating heteroclinic connections between quasi-periodic orbits typically rely on human-in-the-loop or machine learning techniques to find intersections in sets of data in more than three dimensions. We propose a fully systematic method of generating these connections using an invariant property found in knot theory: the linking number. This method proves to be robust in detecting heteroclinic connections between isoenergetic invariant tori in the circular restricted three-body problem.