Lagrange方程应用于流体动力学

Application of Lagrange equation in fluid mechanics

如何将Lagrange方程应用于流体动力学的问题是一个理论研究的难题。按照从变分学的基本理论研究做起的思想,本文应用变导的概念和运算法则,通过研究Lagrange方程中求导的性质,逐步地将Lagrange方程应用于理想流体动力学。按照从变分学的基本理论研究做起的思想,本文应用Lagrange-Hamilton体系,即非保守系统的Lagrange方程是非保守系统的Hamilton型拟变分原理的拟驻值条件,由不可压缩黏性流体动力学的Hamilton型拟变分原理推导出不可压缩黏性流体动力学的Lagrange方程,进而应用不可压缩黏性流体动力学的Lagrange方程推导出不可压缩黏性流体动力学的控制方程。探讨将Lagrange方程应用于可压缩黏性流体动力学问题中,推导出可压缩黏性流体动力学的控制方程。本文解决了如何将Lagrange方程应用于流体动力学的问题。

The application of the Lagrange equation to fluid dynamics is difficult in theoretical research. In accordance with basic theory research on the calculus of variations, the concept of the variational derivative and algorithm are applied. The Lagrange equation is applied to ideal fluid dynamics gradually by studying the property of derivation from the Lagrange equation. The Lagrange-Hamihon system, which is the Lagrange equation of a non-conservative system, is a quasi-stationary condition of Hamilton-type quasi-variational principle of a non-conservative system. The Lagrange equations for incompressible viscous fluid dynamics are derived from the Hamihonian quasi-variational principle of the incompressible viscous fluid dynamics successfully. The governing equations of incompressible viscous fluid dynamics are deduced from the Lagrange equation of incompressible viscous fluid dynamics. Finally, application of the Lagrange equation to the questions of compressible viscous fluid dynamics is discussed. This paper comprehensively describes how to apply the Lagrange equation to fluid dynamics.