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Hohmann transfer via constrained optimization

  • Li XieEmail author
  • Yi-qun Zhang
  • Jun-yan Xu
Article

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.

Key words

Hohmann transfer Nonlinear programming Constrained optimization Calculus of variations 

CLC number

O232 V412.4 

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Copyright information

© Editorial Office of Journal of Zhejiang University Science and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, School of Control and Computer EngineeringNorth China Electric Power UniversityBeijingChina
  2. 2.Beijing Institute of Electronic Systems EngineeringBeijingChina

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