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Solution for Nonlinear Three-Dimensional Intercept Problem with Minimum Energy
Joint Authors
Leeghim, Henzeh
Kim, Donghoon
Turner, James
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-26
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
Classical orbit intercept applications are commonly formulated and solved as Lambert-type problems, where the time-of-flight (TOF) is prescribed.
For general three-dimensional intercept problems, selecting a meaningful TOF is often a difficult and an iterative process.
This work overcomes this limitation of classical Lambert’s problem by reformulating the intercept problem in terms of a minimum-energy application, which then generates both the desired initial interceptor velocity and the TOF for the minimum-energy transfer.
The optimization problem is formulated by using the classical Lagrangian f and g coefficients, which map initial position and velocity vectors to future times, and a universal time variable x.
A Newton-Raphson iteration algorithm is introduced for iteratively solving the problem.
A generalized problem formulation is introduced for minimizing the TOF as part of the optimization problem.
Several examples are presented, and the results are compared with the Hohmann transfer solution approaches.
The resulting minimum-energy intercept solution algorithm is expected to be broadly useful as a starting iterative for applications spanning: targeting, rendezvous, interplanetary trajectory design, and so on.
American Psychological Association (APA)
Leeghim, Henzeh& Kim, Donghoon& Turner, James. 2013. Solution for Nonlinear Three-Dimensional Intercept Problem with Minimum Energy. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-1009390
Modern Language Association (MLA)
Leeghim, Henzeh…[et al.]. Solution for Nonlinear Three-Dimensional Intercept Problem with Minimum Energy. Mathematical Problems in Engineering No. 2013 (2013), pp.1-8.
https://search.emarefa.net/detail/BIM-1009390
American Medical Association (AMA)
Leeghim, Henzeh& Kim, Donghoon& Turner, James. Solution for Nonlinear Three-Dimensional Intercept Problem with Minimum Energy. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-1009390
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1009390