Abstract
Recently, there has been accelerated interest in missions utilizing trajectories near libration points. The trajectory design issues involved in missions of such complexity go beyond the lack of preliminary baseline trajectories (since conic analysis fails in this region of the solution space). Successful and efficient design of mission options will require new persepectives; a more complete understanding of the solution space is imperative. In this investigation, dynamical systems theory is applied to better understand the geometry of the phase space in the three-body problem via stable and unstable manifolds. Then, the manifolds are used to generate various solution arcs and establish trajectory options that are then utilized in preliminary design for the proposed Suess-Urey mission.
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References
GÓMEX, G., JORBA, A., MASDEMONT, J., and SIMÓ, C. “Final Report: Study Refinement of Semi-Analytical Halo Orbit Theory,” ESOC Contract Report, Contract No. 8625/89/D/MD(SC), Barcelona, Spain, April 1991.
GÓMEZ, G., JORBA, A., MASDEMONT, J., and SIMÓ, C. “Study of the Transfer from the Earth to a Halo Orbit Around the Equilibrium Point L1,” Celestial Mechanics and Dynamical Astronomy, Vol. 56, No. 4, 1993, pp. 541–562.
GÓMEZ, G., JORBA, A., MASDEMONT, J., and SIMÓ, C. “Moon’s Influence on the Transfer from the Earth to a Halo Orbit Around L1,” Predictability, Stability, and Chaos in N-Body Dynamical Systems (A.E. Roy, editor), Plenum Press, New York, 1991, pp. 283–290.
HOWELL, K. C., MAINS, D. L., and BARDEN, B. T. “Transfer Trajectories from Earth Parking Orbits to Sun-Earth Halo Orbits,” Paper No. 94–160, AAS/AIAA Flight Mechanics Conference, Cocoa Beach, Florida, February 1994.
BARDEN, B. T. “Using Stable Manifolds to Generate Transfers in the Circular Restricted Problem of Three Bodies,” M. S. Thesis, School of Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana, December 1994.
HOWELL, K. C., and PERNICKA, H. J. “Numerical Determination of Lissajous Trajectories in the Restricted Three-body Problem,” Celestial Mechanics, Vol. 41, Nos. 1–4, 1988, pp. 107–124.
MARCHAL, C. “Study on the Analytic Representation of Halo Orbits,” ESA Contractor Final Report, Contract Report No. 5647/83/D/JS(SC), Châtillon, France, July 1985.
RICHARDSON, D. L. “Analytic Construction of Periodic Orbits About the Collinear Points,” Celestial Mechanics, Vol. 22, No. 3, 1980, pp. 241–253.
WIGGINS, S. Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York, 1990.
GUCKENHEIMER, J., and HOLMES, P. Nonlinear Oscillations, Dynamical Systems, and Bi-furcations of Vector Fields, Springer-Verlag, New York, 1983.
PARKER, T. S., and CHUA, L. O. Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, New York, 1989.
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A previous version of this paper was presented at the AIAA/AAS Astrodynamics Specialists Conference, San Diego, California, July 1996.
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Howell, K.C., Barden, B.T. & Lo, M.W. Application of Dynamical Systems Theory to Trajectory Design for a Libration Point Mission. J of Astronaut Sci 45, 161–178 (1997). https://doi.org/10.1007/BF03546374
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DOI: https://doi.org/10.1007/BF03546374