Generalized Coordinates definition of Generalized Coordinates in the Free Online Encyclopedia.

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 q_i (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 q_i = q_i(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.

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No references found			n-1] are the generalized coordinates and the time derivatives of these coordinates. Virtual environment for manipulating microscopic particles with ... by LeBrun, Thomas W. / Journal of Research of the National Institute of Standards and Technology			General Strike of 1903 in Southern Russia General Strike of 1926 in Great Britain General Strike of 1968 in France general supplies general term General Theory of Relativity general topology general transcription factor General Union of Workers General-in-Chief general-purpose automatic test system general-purpose bomb General-Purpose Computer general-purpose controller general-purpose function generator General-purpose Hall for Entertaining and Sports general-purpose language general-purpose systems simulation general-purpose vehicle general-support artillery Generalic, Ivan Generalissimo Generalization generalized anxiety disorder generalized binomial trials model Generalized Coordinates generalized Euclidean space generalized feasible flow generalized force Generalized Forces generalized function Generalized Functions generalized hydrostatic equation generalized max-flow min-cut theorem generalized mean-value theorem Generalized Momenta generalized momentum generalized permutation generalized Poincaré conjecture generalized power generalized program generalized ratio test generalized routine generalized s-t cut generalized s-t network generalized system generalized transmission function generalized velocity generally accepted standard Generalov, Fedor Generalov, Fedor Stepanovich			Generalized Cascaded Quadruplet Generalized Center of Pressure Generalized Cerebellar Model Articulation Controller Generalized Coding Generalized cohomology theories Generalized cohomology theory Generalized Common Contract Language Generalized Complementary Flux Condition Generalized Complex Orthogonal Design Generalized Compound Generalized Conjugate Gradient Generalized Conjugate Residual Generalized Conjugate Residual Method with Inner Orthogonalization Generalized Consecutive System Generalized Constant Modulus Algorithm Generalized Constant Modulus Criteria Generalized Constrained-Minimum Mean Output Energy Receiver Generalized Context Tree Generalized Context-Free Grammar Generalized Continuum Hypothesis Generalized Convective Available Potential Energy Generalized Conversational Implicature Generalized Convulsive Status Epilepticus Generalized coordinate Generalized Coordinates generalized cortical hyperostosis generalized cortical hyperostosis generalized cortical hyperostosis Generalized Cost Effectiveness Analysis Generalized Coupling Model Generalized Cross Validation Generalized Cross-Correlation Function Generalized Cullen number Generalized Cullen prime Generalized Data Retrieval Generalized Data Stream Generalized Decision-Feedback Equalizer Generalized Diatomics-In-Molecules generalized differential quadrature Generalized Differential Quadrature Rule generalized differential quotient Generalized Diffie-Hellman Problem Generalized Digital Environmental Model Data Base Generalized Digital Waveguide Networks Generalized dihedral group Generalized dihedral group Generalized Discrete Fourier Transform Generalized discrete logarithm problem Generalized Discrete Multi-Tone generalized disease generalized disease generalized disease generalized disease Generalized Distorted-Wave Born Generalized Distributed Constrained Power Control