In analytical mechanics, specifically the study of the rigid body dynamics of multibody systems, the term generalized coordinates refers to the parameters that describe the configuration of the system relative to some reference configuration. These parameters must uniquely define the configuration of the system relative to the reference configuration.
An example of a generalized coordinate is the angle that locates a point moving on a circle, in contrast to its x and y coordinates. The adjective "generalized" distinguishes these parameters from the traditional use of the term coordinate as measured against a specified line, such as Cartesian coordinates .
Parameters that are convenient for the specification of the configuration of a system are selected to be generalized coordinates. If these parameters are independent of one another, then number of independent generalized coordinates is defined by the number of degrees of freedom of the system.
The generalized velocities are the time derivatives of the generalized coordinates of the system.
Read more about Generalized Coordinates: Simple Pendulum, Double Pendulum, Constraint Equations, Generalized Coordinates and Virtual Work
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