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Leveraging quasi-periodic orbits for trajectory design in cislunar space

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A Correction to this article was published on 11 February 2022

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Abstract

Incorporating quasi-periodic orbits into the preliminary design process offers a wide range of options to meet mission constraints and address the challenges in a complex trade space. In this investigation, linear stability and quasi-periodic orbit family continuation schemes are examined to meet various types of constraints. Applications in eclipse avoidance and transfer design are examined by leveraging quasi-periodic orbits and their associated hyperbolic manifolds in the lunar region. Solutions are transitioned to an ephemeris model to validate that geometries are maintained in higher-fidelity models. When the natural dynamical structures associated with quasi-periodic orbits are leveraged, novel trajectory solutions can emerge.

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Acknowledgments

The authors thank the Purdue University School of Aeronautics and Astronautics and the Rune and Barbara Eliasen Visualization Laboratory for the use of facilities and for financial support. The authors also thank the Purdue Multi-body Dynamics Research Group for insightful discussions about quasi-periodic orbits.

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Authors and Affiliations

  1. School of Aeronautics and Astronautics, Neil Armstrong Hall of Engineering, West Lafayette, IN, 47907-2045, USA

    Brian P. McCarthy & Kathleen C. Howell

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  1. Brian P. McCarthy
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Correspondence to Brian P. McCarthy.

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Brian McCarthy is currently a Ph.D. student in the School of Aeronautics and Astronautics at Purdue University. In 2014, he graduated from Virginia Tech with a double major in aerospace and ocean engineering and a minor in mathematics. After graduating from Virginia Tech, he worked for two years as a flight dynamics analyst on the Aqua, Aura, Terra, and TRMM missions at NASA Goddard Space Flight Center (GSFC). During his time at GSFC, he received a NASA Group Achievement Award for his efforts during decommissioning of the TRMM spacecraft. Brian began as a full-time graduate research assistant at Purdue University in the fall of 2016 and received his M.S. degree in December of 2018. His research area focuses on applying dynamical systems techniques to trajectory design in multi-body environments. He most recently worked with NASA Johnson Space Center on trajectory and mission design for the Lunar Gateway and Artemis programs.

Kathleen Howell is currently the Hsu Lo Distinguished Professor of Aeronautics and Astronautics in the College of Engineering at Purdue University. She earned her B.S. degree in aerospace engineering from Iowa State University. Her M.S. and Ph.D. degrees in aeronautical and astronautical Sciences are from Stanford University. Professor Howell’s technical research focus is astrodynamics in complex gravitational environments. She has successfully applied these methodologies to numerous NASA missions. Her contributions include mission planning and trajectory optimization, station-keeping and maneuver design, low-thrust applications that include small satellites, and the development of interactive visual capabilities for complex mission scenarios. As a principal investigator, she has obtained numerous grants and received various awards related to her research program and in recognition as an engineering educator. She served for many years as the Editor-in-Chief for the AAS Journal of the Astronautical Sciences; she is also a member of other editorial boards. Professor Howell is a member of the National Academy of Engineering, the American Academy of Arts and Sciences, the Celestial Mechanics Institute, and the International Academy of Astronautics. She is also a Fellow of both AIAA and AAS. She is involved with various other organizations within the international aerospace and astrodynamics community.

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McCarthy, B.P., Howell, K.C. Leveraging quasi-periodic orbits for trajectory design in cislunar space. Astrodyn 5, 139–165 (2021). https://doi.org/10.1007/s42064-020-0094-5

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