# Damping matrix

In applied mathematics, a damping matrix is a matrix corresponding to any of certain systems of linear ordinary differential equations.

A damping matrix is defined as follows. If the system has n degrees of freedom un and is under application of m damping forces.

Each force can be expressed as follows:

$f_{Di}=c_{i1} \dot{u_1}+c_{i2} \dot{u_2}+\cdots+c_{in} \dot{u_n}=\sum_{j=1}^n c_{i,j}\dot{u_j} \,$

It yields in matrix form;

$F_D=C \dot{U} \,$

where C is the damping matrix composed by the damping coefficients:

$C=(c_{i,j})_{1\le i\le n,1\le j\le m} \,$