Generalized Coordinates

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generalized coordinates

[′jen·rə‚līzd kō′ȯrd·ən·əts]
A set of variables used to specify the position and orientation of a system, in principle defined in terms of cartesian coordinates of the system's particles and of the time in some convenient manner; the number of such coordinates equals the number of degrees of freedom of the system Also known as Lagrangian coordinates.

Generalized Coordinates


parameters qi (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 qi = qi(t), where 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.

References in periodicals archive ?
Such change is defined by generalized coordinate [[xi].
The variation law of the mechanism generalized coordinate is experimentally determined.
Fully integrated generalized coordinate support in the core package
The generalized coordinate [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where the first impact appears and velocities of the pellets immediately after the collision [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] the initial conditions of motion of the pellets in the following motion intervals.
i]--current, neutral, maximum and minimum generalized coordinate values, respectively; [gamma].
j]; the final item relates to a constraint equation and a Lagrangian multiplier which express a constraining force in the direction of the generalized coordinate [q.
Known (the data entry program developed in Maple): lengths of kinematic elements of the mechanism in mm, kinematic elements masses [kg], and the mechanical moments of inertia, law of variation of generalized coordinate established by the experimental question, respectively:
The displacements obtained have units of measure--meter and for linear generalized coordinate [[theta].
i] corresponds to each generalized coordinate in the equation of motion.
8) while moving its CT with force exerted by it if laws of change manipulator's generalized coordinates [q.

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