中文摘要：

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.

英文摘要：

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.