Degree of freedom (mechanics)

Article By:

Fisher, Russell A. Department of Physics, Northwestern University, Evanston, Illinois.

Last reviewed:January 2020

DOI:https://doi.org/10.1036/1097-8542.183800

Any one of the number of independent ways in which the space configuration of a mechanical system may change. A material particle confined to a line in space can be displaced only along the line, and therefore has one degree of freedom. A particle confined to a surface can be displaced in two perpendicular directions and accordingly has two degrees of freedom. A particle free in physical space has three degrees of freedom corresponding to three possible perpendicular displacements. A system composed of two free particles has six degrees of freedom, and one composed of N free particles has 3N degrees. If a system of two particles is subject to a requirement that the particles remain a constant distance apart, the number of degrees of freedom becomes five. Any requirement which diminishes by one the degrees of freedom of a system is called a holonomic constraint. Each such constraint is expressible by an equation of condition which relates the system's coordinates to a constant, and may also involve the time. When applied to systems of particles, a holonomic constraint frequently has the geometrical significance of confining a particle to a specified surface, which may be time-dependent. See also: Constraint

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