# Degrees of freedom

From AMS Glossary

## degrees of freedom

In an unconstrained dynamic or other system, the number of independent variables required to specify completely the state of the system at a given moment.

If the system has constraints, that is, kinematic or geometric relations between the variables, each such relation reduces by one the number of degrees of freedom of the system. In a continuous medium with given boundary conditions, the number of degrees of freedom is the number of normal modes of oscillation. Thus, a particle moving in space has three degrees of freedom; an incompressible fluid with a free surface has an infinite number of degrees of freedom.