GALCIT Colloquium

The application of dynamical systems methods to the design of spacecraft trajectories has resulted in a robust and rich approach to developing transfers in multi-body problems. Perhaps the most elegant approach to these designs are the use of invariant orbits and their stable and unstable manifolds to effect transfers that can move across large distances in space. Examples of these approaches include the Genesis and Artemis missions. Most specific applications in this realm have focused on using simple invariant orbits such as periodic orbits and their manifolds to find candidate heteroclinic connections. However, the existence of higher-dimensional invariant orbits such as quasi-periodic orbits and their related manifolds has not been studied as closely, due to the difficulty in precisely computing these objects in general situations.

Recent research at the University of Colorado (CU) has developed a robust computational algorithm for precisely finding and continuing quasi-periodic orbits of dimension 2 and higher, along with their manifolds (Z. Olikara, PhD. Thesis, 2016). The use of these higher-dimensional orbits can have significant impact on the design of heteroclinic transfers, along with many other applications. This arises due to the relatively high phase space co-dimensions of the stable and unstable manifolds of these orbits, making it is easier to find connections between different quasi-periodic tori of the same energy. Similarly, the ability to compute these higher-dimensional tori also enables the robust continuation of periodic orbits and tori in periodically perturbed problems, such as the elliptic-restricted 3-body problem or the problem of orbiting about an asteroid in a complex rotation state. There are also significant applications to orbit mechanics in complex environments and formation flight of satellites (N. Baresi, PhD. Thesis, 2017). This talk will describe our recent, current and future research on these problems.