Three-dimensional closed-form costate solutions in optimal coast

被引：10

作者：

Pan, Binfeng ^{[2
,3
]}

Lu, Ping ^{[1
]}

Chen, Zheng ^{[2
]}

机构：

[1] Iowa State Univ, Dept Aerosp Engn, Ames, IA 50011 USA

[2] NW Polytech Univ, Sch Astronaut, Xian 710072, Shaanxi, Peoples R China

[3] Natl Key Lab Aerosp Flight Dynam, Xian 710072, Shaanxi, Peoples R China

来源：

ACTA ASTRONAUTICA | 2012年 / 77卷

关键词：

Optimal space trajectories; Trajectory optimization; Orbital transfers; ORBITAL TRANSFERS; LAGRANGIAN MULTIPLIERS; SWITCHING FUNCTION; PRIMER VECTOR; TRAJECTORIES; PERIODS; ARCS;

D O I：

10.1016/j.actaastro.2012.04.009

中图分类号：

V [航空、航天];

学科分类号：

08 ; 0825 ;

摘要：

The costate along a coast arc on an optimal space trajectory contains critically important information about the trajectory. For free-time fuel-optimal flight, the costate at the start of the coast determines completely the optimal length of the coast. Yet most closed-form solutions for costate under various coordinate systems available in the literature are only for two-dimensional flight. In this paper complete three-dimensional closed-form costate solutions in flight-path coordinate system are derived for all conic orbits. These results, as an example of their practical usefulness, enable the optimal duration of any non-circular Keplerian coast arc to be accurately determined from the appropriate root of a polynomial of 5th degree in true anomaly, and a 4th degree polynomial for circular orbits. The value of the development in the paper is demonstrated by solving two relatively difficult multi-finite-burn orbital transfer problems. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：156 / 166

页数：11

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