# 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 ?
The problem of dynamics mechanisms with non-linear function of the position (especially in multimass systems, in systems that form branched and closed circuits) the expression of kinematic and potential energies through independent generalized coordinates leads to complex functional relations.
Since multitethered chain-type satellite system consists of N satellites connected by N - 1 tethers in a chain configuration, the dynamics of the model could be described by 3 N generalized coordinates.
Based on the two-piece dumbbell model, the generalized coordinates are [R.
i]--are generalized coordinates for the system with n degrees of freedom, [E.
He describes such concepts as generalized coordinates, constraints, the D'Alembert principle, and Euler-Lagrange's and Hamilton's equations.
The former can be described by the prosthesis joint angles, and the latter by joint angles combined with a set of generalized coordinates locating the center of mass and principal axes of the prosthesis relative to an inertial reference frame.
8) while moving its CT with force exerted by it if laws of change manipulator's generalized coordinates [q.
To ensure mathematical correctness of the problem solution, we rewrite this equation in a system of generalized coordinates ([[xi].
k,z]--position vectors directed along axes x, y and z respectively); i--the number of generalized coordinates (i = 0, .
For this study, generalized coordinates predominantly represent the articulation of the dancers' joints, and the generalized forces are predominantly the torques at the corresponding joints.
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.

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