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Stretching in phase space and applications in general nonautonomous multi-body problems

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Abstract

In the circular restricted three-body problem, periodic orbits, stable and unstable manifolds, chaotic regions, and other dynamical features have all proven useful for engineering applications. These phase-space structures can be identified because the system is autonomous in a rotating frame. In more complex multi-body and high-fidelity models, classic invariant sets are not readily identifiable and new approaches are required. The approach here exploits the anisotropy of the growth or decay of perturbations to the trajectories, building on recent ideas from the theory of hyperbolic Lagrangian coherent structures. The present framework yields a mechanism to construct transfers in multi-body systems. In particular, it is applied to a restricted four-body problem and transfers are constructed requiring smaller \(\varDelta v\) values than are necessary to accomplish the corresponding shift in Jacobi constant values for the associated embedded three-body problems.

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Acknowledgments

The authors wish to acknowledge the insight and assistance of Dr. Amanda Haapala and Ms. Natasha Bosanac with the numerical corrections of trajectories as well as Mr. Rohan Sood for proofreading the document. This work is supported by the Rune and Barbara Eliasen Aerospace Visualization Laboratory at Purdue University. The facilities of the Eliasen lab have been leveraged heavily for computation and the production of visuals for this paper. Support for this effort from the Purdue University College of Engineering is also acknowledged and appreciated.

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Authors and Affiliations

  1. School of Aeronautics and Astronautics, Purdue University, 701 West Stadium Avenue, West Lafayette, IN, 47907-2045, USA

    Cody R. Short & Kathleen C. Howell

  2. Department of Mechanical and Process Engineering, Institute for Mechanical Systems, ETH Zurich, Leonhardstrasse 21, Zürich, Switzerland

    Daniel Blazevski & George Haller

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  1. Cody R. Short
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  2. Daniel Blazevski
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  3. Kathleen C. Howell
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  4. George Haller
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Correspondence to Cody R. Short.

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Short, C.R., Blazevski, D., Howell, K.C. et al. Stretching in phase space and applications in general nonautonomous multi-body problems. Celest Mech Dyn Astr 122, 213–238 (2015). https://doi.org/10.1007/s10569-015-9617-4

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