# Generalized Coordinates

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## generalized coordinates

[′jen·rə‚līzd kō′ȯrd·ən·əts]## Generalized Coordinates

parameters *q _{i}* (

*i*= 1, 2, …,

*s*) that have any dimension, are mutually independent, and are equal in number to the number

*s*of degrees of freedom of a mechanical system for which they uniquely determine the position. The law of motion for a system in generalized coordinates is given by

*s*equations of the type

*q*=

_{i}*q*), where

_{i}(t*t*is time.

Generalized coordinates are used in the solution of many problems, especially when a system is subject to constraints on its motion. In this case, the number of equations describing the motion of the system is substantially reduced in comparison with, for instance, the equations in Cartesian coordinates. In systems having an infinitely large number of degrees of freedom, such as a continuous medium or a physical field, the generalized coordinates are particular functions of the space and time coordinates and are given special names, such as potentials and wave functions.