显示多体动力学方程自动编制技术

Automatically generating explicit equations of motion for multi-body systems

为高效得到复杂柔性多体航天器的动力学方程解析表达式,研究了系统动力学方程自动编制技术。首先,基于Kane方法推导了构型简单的链状多体系统动力学显式方程;然后,根据方程中各项物理意义和分布规律,开发了适用于树状构型多体航天器的解析动力学方程输出程序,并运用Latex软件对输出文本进行二次编译,增强输出复杂数学公式的可读性。所得方法极大地简化了对此类航天器的建模工作。

The development of the complex multibody spacecraft raises higher requirement to multi-body dynamics modeling and control technology.The explicit dynamics equations of the system are always needed to analyze system′s characteristics and design controllers,but the complexity of system brings difficulty to deriving the equations.In order to solve this problem,the explicit form of dynamics equations′analytical expression was inferred by using Kane′s method,the chain structure system′s explicit dynamics equations;then,by analyzing this equation,physical meaning and regularities of distribution of each equation item were established;using those regularities, a program that can output the explicit dynamics equations of spacecraft system with tree structure was developed.This program reduces the workload of modeling this type of spacecraft significantly.