分析力学初值问题的一种变分原理形式  

A VARIATIONAL PRINCIPLE FORM FOR INITIAL VALUE PROBLEMS IN ANALYTICAL MECHANICS

作　　者：梁立孚[1] 罗恩[2] 冯晓九[3] 

机构地区：[1]哈尔滨工程大学建筑学院,哈尔滨150001 [2]中山大学应用力学与工程系,广州510275 [3]黑龙江科技学院数力系,哈尔滨150027

出　　处：《力学学报》2007年第1期106-111,共6页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10272034;10172098);博士点基金(20030558025)资助项目.~~

摘　　要：明确了分析力学初值问题的控制方程,按照广义力和广义位移之间的对应关系,将各控制方程卷乘上相应的虚量,代数相加,进而在原空间中建立了分析力学初值问题的一种变分原理形式,即建立了分析力学初值问题的卷积型变分原理和卷积型广义变分原理．推导了分析力学初值问题卷积型变分原理和卷积型广义变分原理的驻值条件．在建立分析力学初值问题的一种变分原理形式的同时,将变积方法推广为卷变积方法．According to relations between generalized forces and generalized displacements, convolution are performed between the governing equations of initial value problems in the primary space and the corresponding virtual quantities, and results are added algebraically. A variational principle form for initial value problems in analytical mechanics are then established in the original space, i.e. the variational principles and generalized variational principles in convolution form for initial value problems in analytical mechanics are established in the original space. The stationary conditions of the variational principles and generalized variational principles are deduced. In the meantime, the variational integral method is generalized into the convolutional variational integral method. Using these variational principles and generalized variational principles for initial value problems in analytical mechanics, we can establish models of finite element method and other approximate calculation method and can also find exact solutions of initial value problems in analytical mechanics and transform differential equations into algebraic equations.

关 键 词：分析力学 变分原理 初值问题 变积方法 广义力 广义位移 

分 类 号：O316[理学—一般力学与力学基础]