Application of dynamical systems theory in mission design and conceptual development for libration point missions

Brian Todd Barden, Purdue University

Abstract

The space missions that are currently being proposed are growing increasingly demanding from a mission design perspective. Existing design tasks must be accomplished in a more efficient manner, and new missions concepts must also be facilitated. This study addresses two fundamental issues: transfer design to and from libration point orbits, and conceptual development for new missions in the context of the three-body problem. First, transfer trajectories and mission design within the context of more complicated dynamical models is approached using dynamical systems theory, and the work presented here builds from previous advances made within the framework of the circular restricted three-body problem. In particular, invariant stable and unstable manifolds associated with libration point trajectories are computed to establish a set of solution arcs, each with a dynamical significance, from which a complete mission may be constructed by patching together various selected solution arcs. This process is initially developed in and applied to the circular restricted model, but it is then extended to more complicated dynamical models. The complete process is demonstrated via the mission design of NASA's Discovery class mission, Genesis. The second issue of interest is conceptual development for new mission scenarios. Again, dynamical systems theory is utilized to heighten intuition and understanding. This time, the focus is on fundamental motions near collinear libration points. These motions and their relationships to each other are considered in the context of the center manifold. In doing so, a new mission concept of flying multiple spacecraft in formation near a libration point emerges. Specifically, a configuration is established such that some number of spacecraft will naturally remain in formation (ideally without control). As before, this concept is investigated first in the circular restricted problem, then the investigation is extended to the real system. Once the natural motions observed in the circular restricted problem are verified to exist in the real model, other configurations specified independent of the dynamics, termed non-natural configurations, are considered. This leads to a discussion of some of the pertinent issues in controlling such configurations. Both discrete and continuous control options are investigated.

Degree

Ph.D.

Advisors

Howell, Purdue University.

Subject Area

Aerospace materials

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