degree of freedom

degree of freedom [di′grē əv ′frē·dəm]

(mechanics)

Any one of the number of ways in which the space configuration of a mechanical system may change.

Of a gyro, the number of orthogonal axes about which the spin axis is free to rotate, the spin axis freedom not being counted; this is not a universal convention; for example, the free gyro is frequently referred to as a three-degree-of-freedom gyro, the spin axis being counted.

(physical chemistry)

Any one of the variables, including pressure, temperature, composition, and specific volume, which must be specified to define the state of a system.

(statistics)

A number one less than the number of frequencies being tested with a chi-square test.

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Degree of freedom (mechanics)

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. See Constraint