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 ?
Choosing the angle of rotation the driving link of the mechanism for the generalized coordinate [q.
6), we can obtain the co-energy in d-q frame, which is expressed by generalized coordinate [Z.
r] are the mass matrix, stiffness matrix, and exciting force vector based on generalized coordinate [x.
The reduction is carried out as a function of the generalized coordinate and it is independent of time and velocity of the system.
Such change is defined by generalized coordinate [[xi].
Q = the generalized force applied to the ith generalized coordinate
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.
The variation law of the mechanism generalized coordinate is experimentally determined.
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.
i]--current, neutral, maximum and minimum generalized coordinate values, respectively; [gamma].

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