forTrajectoryDynamics前言摘要Anovelmethodtoevaluatethetrajectorydynamicsoflow-thrustspacecraftisdeveloped.ThethrustvectorcomponentsarerepresentedasFourierseriesineccentricanomaly,andGauss’svariationalequationsareaveragedoveroneorbittodefineasetofsecularequations.Thesesecularequationsareafunctionofonly14ofthethrustFouriercoefficients,regardlessoftheorderoftheoriginalFourierseries,andaresufficienttoaccuratelydeterminealow-thrustspiraltrajectorywithsignificantlyreducedcomputationalrequirementsascomparedwithintegrationofthefullNewtonianproblem.Thismethodhasapplicationstolow-thrustspacecrafttargetingandoptimalcontrolproblems.一种新的求解小推力轨道动力学的方法被开发出来了。推力向量的各坐标用偏近点角表示为傅里叶级数，并且将高斯变分方程平均到整个轨道上来提高久期方程组的精度。这些久期方程组仅仅是14个推力傅里叶系数的函数而忽略初始傅里叶级的次数，这些方程能够精确有效的解决小推力螺旋轨道问题，且与通常的牛顿问题的积分方法相比能大大减少计算量。这一方法应用在小推力航天器的目标确定和最优控制问题中。I.Introduction引言LOW-THRUSTpropulsionsystemsofferanefficientoptionformanyinterplanetaryandEarth-orbitmissions.However,optimalcontrolofthesesystemscanposeadifficultdesignchallenge.Analyticalorapproximatesolutionsexistforseveralspecialcasesofoptimallow-thrustorbit-transferproblems,butthegeneralcontinuous-thrustproblemrequiresfullnumericalintegrationofeachinitialconditionandthrustprofile.Thetrajectoryishighlysensitivetothesevariables;thus,theoptimalcontrollawovertensorhundredsoforbitsofaspiraltrajectoryisoftendifficulttodetermine.小推力推进系统为许多星际航行和地球轨道任务提供了一种高效的新选择。但是这种系统却对最优化控制提出了新的挑战。对于几种特殊的小推力下的轨道转移的最优控制问题已经出现了解析法和数值近似解的方法，但是对于一般的连续推力问题需要对每一个初始条件和推力值进行完全的数值积分。轨道参数的确定往往对这些变量很敏感，因此，（普通的）最优控制法则对于确定螺旋轨道的数十甚至上百个轨道是十分困难的。Analyticalsolutionshavebeendevelopedformanyspecial-casetransfers,suchasthelogarithmicspiral[1–3],Forbes’sspiral[1],theexponentialsinusoid[4,5],thecaseofconstantradialorcircumferentialthrust[6–8],Markopoulos’sKeplerianthrustprograms[9],Lawden’sspiral[10],andBishopandAzimov’sspiral[11].Morerecentsolutionshaveusedthecalculusofvariations[12]ordirectoptimizationmethods[13]todetermineoptimallow-thrustcontrollawswithincertainconstraints.Severalmethodsforopen-loopm