刚体动力学的拟变分原理及其应用  

THE QUASI-VARIATIONAL PRINCIPLES OF RIGID-BODY DYNAMICS AND THEIR APPLICATIONS

作　　者：梁立孚[1] 郭庆勇[1] 

机构地区：[1]哈尔滨工程大学建筑工程学院,哈尔滨150001

出　　处：《力学学报》2010年第2期300-305,共6页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10272034);博士学科点专项科研基金(20060217020);哈尔滨工程大学基础研究基金(HEUF04003)资助项目~~

摘　　要：为了适应航天事业发展的需要,极有必要开展多柔体系统的理论分析.作为应用非保守系统的拟变分原理进行多柔体动力学的理论分析的组成部分,研究了刚体动力学的拟变分原理及其应用:建立了刚体动力学的拟变分原理,推导出刚体动力学的拟变分原理的拟驻值条件;建立了刚体动力学的广义拟变分原理,说明了应用广义拟变分原理求得问题的解析解和数值解的途径;最后,借助算例说明了应用变分方法来研究刚体动力学问题的优越性.The Reference[1]points out that recent studies to solve the problems of flexible multi-body dynamics mainly depend on the numerical,quantitative methods and almost no one involves in the analytical discussion due to the complexity of flexible multi-body configuration.It is unfavorable to profoundly understand the essence of nonlinear mechanics of the system and to predict the feature of overall dynamics of the system. Therefore,it is the need to study theoretical analysis of flexible multi-body system.Of course,this is a very complex problem and it takes a very long time to solve this problem.The research of this paper carries out to adapt this need. For flexible multi-body,if we think that external forces on the deformable body（including body force and surface force） are non-conservative forces,which also lead to non-conservative forces on the rigid body,that is, the resultant force and the resultant couple acting on center of mass are non-conservative generalized forces. This research is to apply the quasi-variational principles of non-conservative system to the theoretical analysis of the flexible multi-body dynamics.Because of the complexity of the problem,it is divided into several subtasks： 1.To study the quasi-variational principles of rigid-body dynamics and their applications.This is the main subject of this paper;2.To study the quasi-variational principles of flexible single-body dynamics and their applications.This subject has been published in＂Science in China＂;3.To study the quasi-variational principles of flexible multi-body dynamics and their applications.This subject has been written in Ph.D.thesis. In this paper,the quasi-variational principles of rigid-body dynamics are established.The quasi-stationary conditions of the quasi-variational principles of rigid-body dynamics are deduced.The generalized quasivariational principles of rigid-body dynamics are established.The approach to seek analytical solution and numerical solution of rigid-body dynamics is illuminated by using generalized

关 键 词：刚体动力学 拟变分原理 非保守系统 控制约束 非完整约束 

分 类 号：O316[理学—一般力学与力学基础]