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TsAGI Science Journal

ISSN 印刷: 1948-2590
ISSN オンライン: 1948-2604

TsAGI Science Journal

DOI: 10.1615/TsAGISciJ.2014012227
pages 509-529

ANALYTICAL SOLUTIONS OF SPACE FLIGHT EQUATIONS WITH LOW THRUST

Valentina Vasilyevna Laricheva
Central Aerohydrodynamic Institute (TsAGI), 1 Zhukovsky Str., Zhukovsky 140180, Russia

要約

The equations of the two-dimensional motion of a spacecraft (SC) in the central gravity field under action of continuous low thrust are transformed to the form of a quasi-linear weakly unsteady system. For such quasi-linear equations the principle of superposition of solutions of inhomogeneous linear equations was generalized by the author, namely, it was shown that the general solution of quasi-linear equations of the SC is composed of a particular singular slow nonperiodic solution and superimposed fast oscillations conditioned by neighboring solutions. For solutions included in the superposition, the adequate asymptotic forms were proposed; thereby a sufficient accuracy of the analytic representation of the general solution describing a multi-turn SC trajectory was reached. The conditions of the existence and stability of the particular singular solution were stated.