Lamé equations of elasticity

Summary

The Lamé equations, also called the Navier–Cauchy equations, govern small deformations of a homogeneous isotropic elastic solid. Their unknown is the displacement field $u$, which tells how far each point of the body moves. The material enters through two constants, the Lamé parameters $\lambda$ and $\mu$. In the static case they form an elliptic system, and the time-dependent version predicts two kinds of elastic waves, pressure waves and shear waves.