Poincaré sections and resonant orbits in the restricted three-body problem

Tatiana Mar Vaquero Escribano, Purdue University

Abstract

The application of dynamical systems techniques to mission design has demonstrated that the use of invariant manifolds and resonant flybys can enable previously unknown trajectory options and potentially reduce the Δ V requirements. In particular, recent investigations related to the Europa Orbiter baseline trajectory design demonstrate that the flyby segment of this trajectory appears to follow the invariant manifolds of 3:4 and 5:6 unstable resonant orbits before capture around Europa. This investigation includes a detailed analysis of planar and three-dimensional unstable resonant orbits as well as techniques for the computation and visualization of the associated invariant manifolds. Poincaré maps are used as an effective tool in the search for unstable resonant orbits and offer an insightful view of their invariant manifolds. These surface-of-sections are utilized to explore the relationship between the resonances and their invariant manifolds and to search for potential resonant transitions. For two specific energy levels and two different systems, a connection exists between the invariant manifolds associated with a number of two-dimensional unstable resonant orbits and this relationship yields transitions between resonances. In addition, a series of apparently resonant homoclinic-type connections in the Jupiter-Europa and Saturn-Titan systems are presented. The results obtained from this investigation may lead to interesting applications for trajectory and mission design.

Degree

M.S.A.A.

Advisors

Howell, Purdue University.

Subject Area

Aerospace engineering

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