For other uses, see homogeneous.

• The quality of having all properties independent of the position, i.e. translation invariance. This is equivalent to shift invariance in system analysis, although here it is most commonly used in linear systems, whereas in physics the distinction is not usually made. See also isotropy for properties independent of direction. In the Lagrangian formalism, homogeneity (in space) implies conservation of momentum, homogeneity in time implies conservation of energy.
• The quality of an equation of having quantities of the same units on both sides. A valid equation in physics must be homogeneous. This can be used to spot errors in calculations. For example, if one is calculating a velocity, units must always combine to ^*/^*. However, if the equation is homogeneous, it doesn't necessarily mean the equation will be true, since it does not take into account numerical factors. However, it is a very powerful tool in finding characteristic units of the problem, see dimensional analysis.

References

• Landau - Lifschitz: "Theoretical physics - I. Mechanics", chapter one.

Homogenitet | הומוגניות | Omogeneità (fisica) | Homogenitet | Homogêneo | Homogen