Dictionary:Christoffel equation

{{#category_index:C|Christoffel equation}} (kris’ tof ∂l) A form of the wave equation for plane waves used for calculating velocity and slowness surfaces:

$\kappa \left(\gamma {\textbf {C}}\gamma ^{T}\right){\textbf {u}}=\rho \omega ^{2}{\textbf {u}}$,

where $\kappa$ is wavenumber, $\gamma$ is the direction cosine matrix, C is the stiffness tensor, u the particle displacement vector, $\rho$ the density, and $\omega$ the angular frequency. The quantity in parentheses is called the Christoffel matrix.