CLC number: O232; V412.4
On-line Access: 2018-12-14
Received: 2018-05-11
Revision Accepted: 2018-07-23
Crosschecked: 2018-11-27
Cited: 0
Clicked: 5913
Li Xie, Yi-qun Zhang, Jun-yan Xu. Hohmann transfer via constrained optimization[J]. Frontiers of Information Technology & Electronic Engineering, 2018, 19(11): 1444-1458.
@article{title="Hohmann transfer via constrained optimization",
author="Li Xie, Yi-qun Zhang, Jun-yan Xu",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="19",
number="11",
pages="1444-1458",
year="2018",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1800295"
}
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%A Jun-yan Xu
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%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1800295
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T1 - Hohmann transfer via constrained optimization
A1 - Li Xie
A1 - Yi-qun Zhang
A1 - Jun-yan Xu
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 19
IS - 11
SP - 1444
EP - 1458
%@ 2095-9184
Y1 - 2018
PB - Zhejiang University Press & Springer
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DOI - 10.1631/FITEE.1800295
Abstract: Inspired by the geometric method proposed by Jean-Pierre MAREC, we first consider the hohmann transfer problem between two coplanar circular orbits as a static nonlinear programming problem with an inequality constraint. By the Kuhn-Tucker theorem and a second-order sufficient condition for minima, we analytically prove the global minimum of the hohmann transfer. Two sets of feasible solutions are found: one corresponding to the hohmann transfer is the global minimum and the other is a local minimum. We next formulate the hohmann transfer problem as boundary value problems, which are solved by the calculus of variations. The two sets of feasible solutions are also found by numerical examples. Via static and dynamic constrained optimizations, the solution to the hohmann transfer problem is re-discovered, and its global minimum is analytically verified using nonlinear programming.
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