Hamilton solution of linearized Navier-Stokes equations in cylindrical coordinate

The view of Hamilton mechanics effectively solved a series of problems showing significant theoretical valve. If the velocities are sufficiently small the motion will be governed by the linearized Navier-Stokes equations and consequently the problem can be solved under Hamilton system. Establishing variation principle of the problem of linearized Navier-Stokes flow based on principle of virtual work, introducing governing equation into duality system by means of original variables and dual variables of the problem formulated by systematic Lagrange function, and then the deduced equation is still Hamilton canonical equation. In the symplectic space, the effective method of mathematical physics such as separation of variables and expanded symplectic eigenvector can be applied to solution of the problem. And through rational analysis, eigen-value and eigen-solution for the problem of linearized Navier-Stokes flow inside circular tubes can be found directly. Calculation examples provide flow characteristics of fluids inside circular tubes and the results show that the method is of extremely high accuracy.