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| 一般力学初值问题两类变量的广义变分原理 | |
| 引用本文： | 冯晓九,梁立孚,胡超.一般力学初值问题两类变量的广义变分原理[J].哈尔滨工业大学学报,2008,40(1):22-24,34. |
| 作者姓名： | 冯晓九 梁立孚 胡超 |
| 作者单位： | 1. 哈尔滨工业大学,航天学院,哈尔滨,150001;黑龙江科技学院,数力系,哈尔滨,150027 2. 哈尔滨工程大学,建筑工程学院,哈尔滨,150001 3. 哈尔滨工业大学,航天学院,哈尔滨,150001 |
| 摘 要： | 为了建立一般力学初值问题两类变量的广义变分原理,首先明确两类变量的基本方程,应用Laplace变换将基本方程变换到像空间,按照广义力和广义位移之间的对应关系,将各基本方程乘上相应的虚量,代数相加,进而建立了一般力学初值问题的像空间中两类变量的广义变分原理.然后,用Laplace逆变换将像空间中的广义变分原理反演到原空间,进而建立了一般力学初值问题的原空间中两类变量的广义变分原理.并以弹性动力学为例,说明了像空间和原空间中的势能函数和余能函数的内涵. |
| 关 键 词： | 一般力学 初值问题 两类变量 广义变分原理 |
| 文章编号： | 0367-6234（2008）01-0022-03 |
| 收稿时间： | 2006-01-12 |
| 修稿时间： | 2006年1月12日 |
Generalized variational principles with two kinds of variables of initial value problems in general mechanics |
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| FENG Xiao-jiu,LIANG Li-fu,HU Chao.Generalized variational principles with two kinds of variables of initial value problems in general mechanics[J].Journal of Harbin Institute of Technology,2008,40(1):22-24,34. | |
| Authors: | FENG Xiao-jiu LIANG Li-fu HU Chao |
| Affiliation: | 1(1.School of Astronautics,Harbin Institute of Technology,Harbin 150001;2.College of Civil Engineering,Harbin Engineering University,Harbin 150001,China;3.Dept.of Mathematics and Mechanics,Heilongjiang Institute of Science and Technology,Harbin 150027) |
| Abstract: | In order to establish the generalized variational principle of initial value problems of two kinds of variables in general mechanics, it should firstly clarify Laplace the basic equation of two kinds of variables. By using transformation, the basic equations of initial value problems of two kinds chanics were transformed into image space. According to corresponding relations of variables in general mebetween general forces and general displacements, the basic equations of initial value problems in the image space were multiplied by corresponding virtual quantifies, added algebraically. Thus the variational principles and generalized variational principles of initial value problems of two kinds of variables in the image space were established. By using Laplace inverse transformation, the generalized variational principles of initial value problems of two kinds of vailables in the original space were established for general mechanics. Finally, the related problems were discussed. |
| Keywords: | general mechanics initial value problem two kinds of variables generalized variational principle |
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