Approximate analytical solutions for threedimensional ascent trajectory of a solid-fuel launch vehicle with time-varying mass flow rate  

作　　者：Qi YU Wanchun CHEN Wenbin YU 

机构地区：[1]School of Astronautics,Beihang University,Beijing 102206,China

出　　处：《Chinese Journal of Aeronautics》2024年第10期275-293,共19页中国航空学报（英文版）

基　　金：Supported in part by National Natural Science Foundation of China(No.62003012);in part by the Young Tulents Support Program funded by Bcihang Univer-sity,China(No.YWF-23-L-702).

摘　　要：In the scenario that a solid-fuel launch vehicle maneuvers in outer space at high angles of attack and sideslip for energy management,Approximate Analytical Solutions(AAS)for the threedimensional(3D)ascent flight states are derived,which are the only solutions capable of considering time-varying Mass Flow Rate(MFR)at present.The uneven MFR makes the thrust vary nonlinearly and thus increases the difficulty of the problem greatly.The AAS are derived based on a 3D Generalized Ascent Dynamics Model(GADM)with a normalized mass as the independent variable.To simplify some highly nonlinear terms in the GADM,several approximate functions are introduced carefully,while the errors of the approximations relative to the original terms are regarded as minor perturbations.Notably,a finite series with positive and negative exponents,called Exponent-Symmetry Series(ESS),is proposed for function approximation to decrease the highest exponent in the AAS so as to reduce computer round-off errors.To calculate the ESS coefficients,a method of seeking the Optimal Interpolation Points(OIP)is proposed using the leastsquares-approximation theory.Due to the artful design of the approximations,the GADM can be decomposed into two analytically solvable subsystems by a perturbation method,and thus the AAS are obtained successfully.Finally,to help implement the AAS,two indirect methods for measuring the remaining mass and predicting the burnout time in flight are put forward using information from accelerometers.Simulation results verify the superiority of the AAS under the condition of time-varying MFR.

关 键 词：Approximate analytical solutions 3D ascent trajectory Solid-fuel launch vehicle Uneven thrust Energy management 

分 类 号：V475.1[航空宇航科学与技术—飞行器设计]