Wednesday, February 15, 2006, 11am - 12pm

Speaker: Dr. Benjamin F. Villac

Abstract:

As scientific requirements for space exploration increase in scope and complexity (and budgets sometimes shrink), space mission designers face new challenges involving more complex design spaces and unexplored trade-offs. Notably, the question of knowing if a set
of design requirements is actually feasible is often an unknown of the problem. Transposed to the realm of spaceflight mechanics, where current missions present longer flight times and single spacecrafts encounter multiple bodies during a mission, classical design methods
based on two-body approximations cannot always be applied and the set of possible transfers meeting some requirements is an open question.

In this talk, a few results related to the analysis of the motion of a spacecraft in the environment of a moon of Jupiter will be presented in order to illustrate how dynamical system theory ideas can help in extracting global information on an orbital environment
and designing more cost effective transfers.

The first case considered shows how physically based surfaces of section can give a quick overview of important dynamical constraints present in a system. As we know, fixing the energy of a conservative system restricts the space of allowable motion of a spacecraft.
Similarly, it is shown that the surfaces of closest approach from a center of gravity (periapsis surfaces) delimit different types of allowable motion and allow for the proof of (non)existence of certain trajectories.

The second example presented will extend the above idea to the problem of designing large plane change maneuvers. The use of dynamical maps based on the successive iterations of the flow of trajectories with a periapsis surface results in the reduction of the cost of the maneuvers and indicates the constraints imposed by the natural dynamics on the control of a spacecraft.

Finally, a last example considers further the idea of mapping the dynamics by considering chaoticity indicators in order to represent a large class of transfers between separated regions of phase space based on unstable periodic orbits. While libration point missions
(e.g., Soho, Genesis) showed the usefulness of the manifold structures associated with some unstable periodic orbits, such transfer are not limited to libration point missions and the connections relating several unstable periodic orbits can be used as the backbone of complex, but cost effective, transfers. Maps based on fast Lyapunov indicators are shown to reveal the web of connection existing between such orbits in the large.