ABSTRACT
This chapter employs classical mechanics to the description of continuous media, with an emphasis on problems not usually seen in traditional texts. It starts with waves on strings, making them realistic by including friction, variable tension and density, and ultimately nonlinear effects. The chapter covers shock waves and their extension to solitary waves, as described by the Korteweg-de Vries and the Sine-Gordon equations. These extensions of the wave equation produce fascinating results. The chapter deals with hydrodynamics as described by the Navier-Stokes equation. Boundary conditions for hydrodynamic flow can be challenging. Solution of the hydrodynamic equations is made easier by the introduction of two potentials from which the velocity is obtained by differentiation. In 1961 Edward Lorenz used a simplified version of the hydrodynamic equations including convection, viscosity, and gravity to predict weather patterns.
