非保守系统的Lagrange方程  

Lagrange equation of non-conservative systems

作　　者：周平[1,2] 梁立孚[3] 

机构地区：[1]哈尔滨工程大学机电工程学院,黑龙江哈尔滨150001 [2]黑龙江科技大学机械工程学院,黑龙江哈尔滨150022 [3]哈尔滨工程大学航天与建筑工程学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2017年第3期452-459,共8页Journal of Harbin Engineering University

基　　金：国家自然科学基金项目(10272034)

摘　　要：如何将Lagrange方程应用于连续介质动力学,一直是学术界关注的理论课题。如何将Lagrange方程应用于非保守连续介质动力学的问题的研究难度更大。本文应用Lagrange-Hamilton体系,非保守系统的Lagrange方程是非保守系统的Hamilton型拟变分原理的拟驻值条件,成功地将Lagrange方程应用于非保守连续介质动力学。进而应用非保守系统的Lagrange方程推导出非保守连续介质动力学的控制方程,为研究非保守连续介质动力学开辟了一条新的有效途径。How to apply the Lagrange equation to continuum dynamics has always been a theoretical subject in the academic field. How to apply the Lagrange equation to the problem of non-conservative continuum dynamics is even more difficult. The Lagrange equation of non-conservative systems is a quasi-stationary condition for the Hamiltonian quasi-variational principle of non-conservative systems using the Lagrange-Hamilton system. In this paper,the L a-grange equation was successfully applied to non-conservative continuum dynamics. Then,the governing equations of non-conservative continuum dynamics were deduced by the Lagrange equation of non-conservative systems,which opens up a new effective way of studying non-conservative continuum dynamics.

关 键 词：连续介质动力学 LAGRANGE方程 非保守系统 拟变分原理 拟驻值条件 Lagrange-Hamilton体系 

分 类 号：O313[理学—一般力学与力学基础]