轴对称蠕流问题双调和方程的Hamilton描述

Hamilton Representations for the Biharmonic Equation of Axisymmetric Creeping Flow

笔者从无穷维Hamilton系统的等价定义出发,用代数方法把轴对称蠕流问题导入到Hamil-ton体系。借助无穷维Hamilton正则系统的定义和偏微分方程Hamilton正则表示的一些成果,把柱坐标下轴对称蠕流问题关于流线函数的双调和方程写成Hamilton正则方程,使双调和方程形式上变成可以分离变量的问题,由此得到辛正交系及按辛正交系展开的广义解析解。该方法不必提前把变量假设为未知函数,也不必求解Lagrange函数和Hamilton泛函,直接从理性角度上给出了问题的解。算例研究了圆管入口流动问题,验证了笔者方法的有效性。

In this paper,the axisymmetric creeping flow problem is solved under Hamilton system by algebraic method.The biharmonic equation of creeping flow in cylindrical coordinate is a linear partial differential equation with variable coefficients which can be transformed into the infinite dimensional Hamilton system so that the Hamilton system is equivalent to the original equation and the introduced variation is as little as possible.This method includes the criterion principle and concretes the canonical infinite dimensional Hamilton representations instead of finding out the Legendre′s transformation and the Hamiltonian.By using the above method,the entry flow into a circular tube is studied,and the corresponding inlet length is equal to 1.2 times the radius of the tube.The results show that the algebra Hamilton method is effective and with high precision.