Minimum-Time Continuous-Thrust Orbit Transfers

To solve the minimum-time orbital transfer problem under continuous thrust, initial values of the Lagrange costates are required in the calculus of variations formulation. Assuming circle-to-circle transfer, expressions are developed for the approximate values of the optimal initial costates, which...

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Bibliographic Details
Published inThe Journal of the astronautical sciences Vol. 45; no. 4; pp. 411 - 432
Main Authors Thorne, James D., Hall, Christopher D.
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.10.1997
Subjects
Boundary value problems
Calculus of variations
Orbital maneuvers
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Summary:To solve the minimum-time orbital transfer problem under continuous thrust, initial values of the Lagrange costates are required in the calculus of variations formulation. Assuming circle-to-circle transfer, expressions are developed for the approximate values of the optimal initial costates, which are then used as starting guesses for the associated two-point boundary value problem. The optimal initial costates are modeled as functions of the thrust and final radius in canonical units. These approximations work for noncircular destination orbits, as well as for noncoplanar transfers. Examples are provided for coplanar and noncoplanar orbital transfers. A dynamic step limiter is also presented which improves convergence in the shooting method.
ISSN:0021-9142
2195-0571
DOI:10.1007/BF03546400