Lambert’s Problem with Multiple Constraints
Publication: Journal of Aerospace Engineering
Volume 35, Issue 5
Abstract
This paper proposes a new method to solve Lambert’s problem with multiple constraints, including the impulse-magnitude constraints, the trajectory-radius constraints, and the terminal-impact-angle constraint. First, the closed-form range of the chordal terminal velocity component for each constraint is derived. Then, the admissible intersection range for all constraints is obtained. Finally, the feasible solutions are solved in the admissible intersection range by using the terminal-velocity-based Lambert algorithm. The 180° case and the multiple-revolution case are also considered. The proposed method can be also extended to the Lambert algorithms with other independent variables. Compared with the typical method of first solving Lambert’s problem and then pruning the solutions that do not satisfy the constraints, the numerical examples show that the proposed method can reduce a lot of computational time.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work is supported in part by the National Natural Scientific Foundation of China (Grant No. 11772104), Key Research and Development Plan of Heilongjiang Province (Grant No. GZ20210120), and the Fundamental Research Funds for the Central Universities.
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Published In
Journal of Aerospace Engineering
Volume 35 • Issue 5 • September 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Feb 28, 2022
Accepted: Apr 25, 2022
Published online: Jun 9, 2022
Published in print: Sep 1, 2022
Discussion open until: Nov 9, 2022
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