Hamilton's principle applied to fluid mechanics
Abstract
Hamilton's principle is rigorously applied to fluid systems to yield initially the equations of motion of a real (compressible, viscous) fluid. The assumptions of incompressibility and inviscidity are considered within the context of the variational principle. The principle is then used directly to obtain equations of motion for various fluid systems. These equations are approximate in that only the first terms of a set of admissible functions are considered; closure of the set leads to exact solutions. The concept of added mass is generated in passing and the variational equivalent of the D'Alembert paradox is examined.
 Publication:

Quarterly Journal of Mechanics and Applied Mathematics
 Pub Date:
 February 1977
 Bibcode:
 1977QJMAM..30..107L
 Keywords:

 Compressible Fluids;
 Equations Of Motion;
 Fluid Mechanics;
 Hamiltonian Functions;
 Variational Principles;
 Viscous Fluids;
 Flow Equations;
 Flow Velocity;
 Incompressible Fluids;
 Inviscid Flow;
 Piston Theory;
 Fluid Mechanics and Heat Transfer