航天器交会的动力学模型与误差分析

An Error Analysis of Dynamic Model for Spacecraft Rendezvous

建立了航天器交会的相对运动模型，定量地分析了各种援动力的影响，导出了建模过程的截断误差，并给出了算例．结果可用于航天器交会过程分析及误差修正．

To the authors' best knowledge, there is no previously published paper on the error analysis of the analytical solution of dynamic model of rendezvous of spacecrafts. In this paper, the authors give such an error analysis in terms of Ax. △y and Ax computable with eq.(10).The authors are highly pleased to find that the mathematical technique of truncation errors can be used to derive eq.(10). Of course eq.(3), which is well known in flight dynamics, is the starting point of such derivation. The authors go back to the dynamic model on which eq.(3) is based. In books on flight dynamics, when the right-hand side of eq.(2) is expanded into Taylor series, only 1-3y / r2 is retained.This is a crucial step in the derivation of eq.(3). Thus when eq.(3) is used, the approximation due to truncation of Taylor series brings unavoidable error. Eq.(10) gives the estimates of error due to such truncation.Finally the authors like to add that some qualitative discussion is given for the secondary errors due to the ncglection of atmospheric resistance, solar light pressure, solar and lunar gravitation and deviation of the earth from a true sphere.