Abstract
Path planning in the circular restricted 3-body problem (CR3BP) is frequently guided by the forbidden regions and manifold arcs. However, when low thrust is employed to modify the spacecraft trajectory, these dynamical structures pulsate with the varying Hamiltonian value. In a combined CR3BP, low-thrust (CR3BP + LT) model, an additional low-thrust Hamiltonian is available that remains constant along low-thrust arcs given suitable assumptions. Accordingly, the analogous low-thrust forbidden regions and manifolds remain static and are useful guides for low-thrust trajectory design. Strategies leveraging these structures and other insights from the CR3BP + LT are explored to construct transit and capture itineraries.
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References
Anderson, R., Lo, M.: Role of invariant manifolds in low-thrust trajectory design. J. Guid. Control Dyn. 32(6), 1921–1930 (2009). https://doi.org/10.2514/1.37516
Bosanac, N., Cox, A.D., Howell, K.C., Folta, D.C.: Trajectory design for a Cislunar cubesat leveraging dynamical systems techniques: the Lunar IceCube mission. Acta Astronaut. 144, 283–296 (2018). https://doi.org/10.1016/j.actaastro.2017.12.025
Conley, C.: Low energy transit orbits in the restricted three-body problem. SIAM Rev. Soc. Ind. Appl. Math. 16, 732–746 (1968). https://doi.org/10.1137/0116060
Cox, A.D.: A dynamical systems perspective for preliminary low-thrust trajectory design in multi-body regimes. Ph.D. thesis, Purdue University (2020)
Cox, A.D., Howell, K.C., Folta, D.C.: Dynamical structures in a combined low-thrust multi-body environment. In: AAS/AIAA Astrodynamics Specialist Conference. Columbia River Gorge, Stevenson, Washington (2017)
Cox, A.D., Howell, K.C., Folta, D.C.: Dynamical structures in a low-thrust, multi-body model with applications to trajectory design. Celest. Mech. Dyn. Astron. 131(12) (2019). 10.1007/s10569-019-9891-7. Available Online
Cox, A.D., Howell, K.C., Folta, D.C.: Trajectory design leveraging low-thrust, multi-body equilibria and their manifolds. J. Astronaut. Sci. 67(3), 977–1001 (2020). https://doi.org/10.1007/s40295-020-00211-6
Farrés, A.: Transfer orbits to l4 with a solar sail in the Earth–Sun system. Acta Astronaut. 137, 78–90 (2017). https://doi.org/10.1016/j.actaastro.2017.04.010
Haapala, A.F., Howell, K.C.: A framework for construction of transfers linking periodic libration point orbits in the Earth–Moon spatial circular restricted three-body problem. Int. J. Bifurcat. Chaos 26(5), 4 (2016). https://doi.org/10.1142/S0218127416300135
Hardgrove, C., Bell, J., Thangavelautham, J., Klesh, A., Starr, R., Colaprete, T., Robinson, M., Drake, D., Johnson, E., Christian, J.: The lunar polar hydrogen mapper (LunaH-Map) mission: mapping hydrogen distributions in permanently shadowed regions of the Moon’s south pole. In: Annual Meeting of the Lunar Exploration Analysis Group, vol. 1863, p. 2035. Columbia, Maryland (2015)
Hernandez, S., Akella, M.: Lyapunov-based guidance for orbit transfers and rendezvous in Levi–Civita coordinates. J. Guid. Control Dyn. (2014). https://doi.org/10.2514/1.62305
McGuire, M.L., Burke, L.M., McCarty, S.L., Hack, K.J., Whitley, R.J., Davis, D.C., Ocampo, C.: Low-thrust cis-lunar transfers using a 40 kw-class solar electric propulsion spacecraft. In: AAS/AIAA Astrodynamics Specialist Conference. Columbia River Gorge, Stevenson, Washington (2017)
Mingotti, G., Topputo, F., Bernelli-Zazzera, F.: Low-energy, low-thrust transfers to the Moon. Celest. Mech. Dyn. Astron. 105, 61–74 (2009). https://doi.org/10.1007/s10569-009-9220-7
Moore, A., Ober-Blöbaum, S., Marsden, J.: Trajectory design combining invariant manifolds with discrete mechanics and optimal control. J. Guid. Control Dyn. 35(5), 1507–1525 (2012). https://doi.org/10.2514/1.55426
Morimoto, M., Yamakawa, H., Uesugi, K.: Periodic orbits with low-thrust propulsion in the restricted three-body problem. J. Guid. Control Dyn. (2006). https://doi.org/10.2514/1.19079
Petropoulous, A., Sims, J.: A review of some exact solutions to the planar equations of motion of a thrusting spacecraft. In: 2nd International Symposium on Low Thrust Trajectories. Toulouse, France (2002)
Simó, C., Gómez, G., Llibre, J., Martínez, R., Rodríguez, J.: On the optimal station keeping control of halo orbits. Acta Astronaut. 15(6–7), 391–397 (1987). https://doi.org/10.1016/0094-5765(87)90175-5
Swenson, T., Lo, M.W., Anderson, B., Gordordo, T.: The topology of transport through planar Lyapunov orbits. In: AIAA SciTech Forum. Kissimmee, Florida (2018)
Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press, New York (1967)
Topputo, F.: Low-thrust non-Keplerian orbits: analysis, design, and control. Ph.D. thesis, Politecnico di Milano (2005)
Acknowledgements
The authors thank the Purdue University School of Aeronautics and Astronautics for their facilities and support, including access to the Rune and Barbara Eliasen Visualization Laboratory. The authors are also very grateful to the Purdue Multi-Body Dynamics Research Group for interesting discussions and ideas and to the reviewers for providing thorough and insightful feedback on this paper. This research is supported by a National Aeronautics and Space Administration (NASA) Space Technology Research Fellowship, NASA Grant NNX16AM40H.
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The content of this paper was first presented at the AAS/AIAA Space Flight Mechanics Meeting in Ka’anapali, Maui, Hawaii, in January 2019. This work is supported by a NASA Space Technology Research Fellowship, NASA Grant NNX16AM40H.
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Cox, A.D., Howell, K.C. & Folta, D.C. Transit and capture in the planar three-body problem leveraging low-thrust invariant manifolds. Celest Mech Dyn Astr 133, 22 (2021). https://doi.org/10.1007/s10569-021-10022-y
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DOI: https://doi.org/10.1007/s10569-021-10022-y