单柔体动力学拟哈密顿原理的推导  

Derivation of quasi-Hamilton's principles of flexible single body dynamics

作　　者：郝名望[1] 叶正寅[1] 

机构地区：[1]西北工业大学翼型叶栅空气动力学国防科技重点实验室,陕西西安710072

出　　处：《广西大学学报（自然科学版）》2010年第6期954-961,共8页Journal of Guangxi University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(10802067)

摘　　要：多柔体动力学对空间探索和宇航事业的发展起着非常重要的作用,而单柔体动力学又是多柔体动力学的基础,目前,人们对航天器动力学的研究,所作的工作在数值算法上较多,真正在解析上和理论上做的工作较少。从现有的文献可以看出,不少学者采用变分原理建立柔体动力学控制方程,尤其是哈密顿原理,并且大多数都是直接综合一般力学的哈密顿原理和弹性力学的势能原理建立柔体动力学的控制方程。本文从单柔体动力学的基本方程(该方程可以由微元法得到)出发,利用变积方法推导出其拟哈密顿原理,再通过对所得的泛函求驻值条件得到单柔体动力学的控制方程,并对其作分析和讨论。Flexible multi-body dynamics plays an important role in the development of space exploration and space navigation while flexible single body dynamics is the basis of flexible multi-body dynamics.At present,the research work of spacecraft dynamics is focused mainly on numerical algorithms,while less endeavor has been paid to the work on basic theories and analytical researches.Reviewing the existing academic literatures,a lot of researchers set up the governing equations of flexible body dynamics by using the variational principle,especially the Hamilton＇s principle,and most of them build these equations by combining the Hamilton＇s principle of general mechanics and the potential energy principle of mechanics of elasticity.This paper,starting from the fundamental equations of single flexible single body dynamics（which is obtained from infinitesimal element method）,derives the quasi-variational principles of flexible single body by using variational integral method and further arrives at the governing equations of flexible single body dynamics by finding the stationary conditions of the functional obtained.Finally the paper presents some analyses and discussions on the governing equations.

关 键 词：变分原理 拟哈密顿原理 单柔体 多柔体 

分 类 号：O316[理学—一般力学与力学基础] O313.3[理学—力学]