变截面弹性管中一维非定常气流的广义变分原理

Generalized Variational Principles for 1-dimensional Unsteady Compressible Flow in a Varying Cross-section

应用坐标变换，在映象平面上，巧妙地把控制方程转化为守恒形式．在此基础上，作者定义了２个新型函数──迹线长度函数Ｙ和能量函数Ω．在应用刘高联系统方法建立广义变分原理时，发现了非常有趣的临界变分现象．并且分析了产生临界变分的原因，最后导得了一维变截面非定常可压缩均熵流动的广义变分原理．

In the image plane, two special functions──pathline length function Y and energy function Ω──have been defined due to the fact that the control equations can be changed into conservative ones by space translation. Interesting variational crisis come across when the Liu' s systematic method was applied to establish the generalized variational principle. The crisis phenomenon comes from the fact that the defined Lagrange mulipliers are relative. And a generalized variational principle for 1-dimensional unsteady compressible flow in a varying cross section has been deduced.