Generalized Coordinates

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generalized coordinates

[′jen·rə‚līzd kō′ȯrd·ən·əts]
(mechanics)
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 ?
8) while moving its CT with force exerted by it if laws of change manipulator's generalized coordinates [q.
k,z]--position vectors directed along axes x, y and z respectively); i--the number of generalized coordinates (i = 0, .
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]--n-dimensional column vectors of generalized coordinates [q.
The equations of motion (Equation (2)) for the rotor bearing system are obtained using a Lagrangian formulation (VANCE, 1988), with X, Y, [alpha] e [beta] as the generalized coordinates of the system and F and M as the generalized forces and moments, respectively.
21) That result is just what one needs for the divergence theorem in a form suitable for generalized coordinates and hence slightly generalized from that in vector calculus, in order to get results independent of the merely conventional choice of coordinates.
The equations of airfoil motion are derived from the Lagrange equations for the generalized coordinates H and [alpha].
n-1] are the generalized coordinates and the time derivatives of these coordinates.
The selection of the schematic of this model is concerned, first of all, with the isolation of subsystems and specification of the structure of connections between them, the determination of the number of degrees of freedom and type of generalized coordinates, necessary for the complete description of processes present in the system (Murashkin, 1977; Veitz, 1972).
where q--m--the measured vector function of the generalized coordinates of the system; y--k--the measured vector function of the outputs of the system; U--l--the measured vector function of disturbances; D--(m x m)--the matrix of the coefficients of the simplified model; G--(m x l)--and C--(k x m)--the assigned matrices.

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