多体分离中初始扰动发展模式的理论分析

Development mode of initial disturbance in multibody separation:Theoretical analysis

以载机-无人机分离系统为研究对象,基于六自由度运动方程,首次建立了初始扰动发展理论分析模型,得到了扰动幅值发展的显式表达,并首次给出了扰动分布的发展模式。研究表明:在对建立的理论分析模型进行求解时,对加速度/角加速度在初始时刻进行三阶Taylor展开即可对扰动发展模式进行准确描述。扰动幅值在速度扰动方向上以线性增长模式为主导,增长率为速度初始扰动的标准差;扰动幅值在其他方向上呈非线性增长模式。扰动施加方向上的分布发展基本模式是初始分布;在其他方向上,加速度/角加速度在初始时刻的Taylor展开零阶项与初始分布一致,但高阶项显著偏离初始分布,随着时间的推进,高阶项逐渐主导整体的扰动分布,并致其逐渐偏离初始分布。

This paper studies the carrier-unmanned aerial vehicle separation system and for the first time establishes a theory analysis model of the initial disturbance development based on the six degrees of freedom equations of motion.The explicit expression of the disturbance amplitude development is obtained,and the development mode of disturbance distribution is presented for the first time.The research shows that a third-order Taylor expansion of the acceleration/angular acceleration at the initial moment provides an accurate description of the disturbance development pattern in solving the established theoretical analytical model.The amplitude of the disturbance is dominated by the linear growth mode in the direction of the velocity disturbance,and the growth rate is the standard deviation of the initial velocity disturbance.The amplitude of disturbance shows a nonlinear growth pattern in other directions.The basic pattern of the distribution development in the direction of disturbance application is the initial distribution,and in other directions,the zero order term of the Taylor expansion of acceleration/angular acceleration at the initial time is consistent with the initial distribution,but the higher-order term significantly deviates from the initial distribution.As time progresses,the higher-order term gradually dominates the overall disturbance distribution,causing it to gradually deviate from the initial distribution.