Degree of freedom

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In classical mechanics, a degree of freedom is each of the generalized coordinates that specify a given configuration of a system. For example, a position in space is specified by three numbers (e.g. the Cartesion coordinates), hence three degrees of freedom are needed for translation. An orientation would be specified by two numbers (e.g. the Eulerian angles).

Often, effective degrees of freedom must be considered. For example, diatomic molecules would need 6 degrees of freedom, 3 for each atom (since these two can be anywhere in the system). However, vibrations are frozen at temperatures below thousands of K, and only 5 effective degrees of freedom are needed. E.g.: three to specify the location of the centre-of-mass, and two angles to specify rotation. (Rotations may also be frozen, but this happens at low temperatures.)


  1. Benjamin Widom "Statistical Mechanics, A Concise Introduction for Chemists" (2002) ISBN 0521009669