Encyclopedia

Lagrange's equations

Lagrange's equations

Equations of motion of a mechanical system for which a classical (non-quantum-mechanical) description is suitable, and which relate the kinetic energy of the system to the generalized coordinates, the generalized forces, and the time. If the configuration of the system is specified by giving the values of f independent quantities q1,…, qf, there are f such equations of motion.

In their usual form, these equations are equivalent to Newton's second law of motion and are differential equations of the second order for the q's as functions of the time t.

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.

Lagrange's equations

[lə′grän·jəz i‚kwā·zhənz]
(mechanics)
Equations of motion of a mechanical system for which a classical (non-quantum-mechanical) description is suitable, and which relate the kinetic energy of the system to the generalized coordinates, the generalized forces, and the time. Also known as Lagrangian equations of motion.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
Mentioned in
References in periodicals archive
The governing equation of the inverted pendulum model can be derived by using Lagrange's equations. The positions of the lump mass m and the cart are written as
An Inverted Pendulum Model Describing the Lateral Pedestrian-Footbridge Interaction
The equations of motion were deduced using Lagrange's equations and solved through the small parameter method to obtain their solutions up to the second order of approximation.
The equations of motion are derived using Lagrange's equation and are considered as a nonlinear system of second-order differential equations.
The Dynamical Behavior of a Rigid Body Relative Equilibrium Position
For this edition they have added 59 new problems, and a new chapter on applying Lagrange's equations to deriving equations of motion.
Dynamics in Engineering Practice, 11th Edition
Firstly, the dynamic model of the flexible links mounted with multiple PZT transducers is formulated using Lagrange's equations and AMM, and the experimental modal tests of the flexible links are implemented to verify the assumed mode shapes.
The general form of Lagrange's equations for elastic generalized coordinates is given as
Active vibration suppression of a 3-DOF flexible parallel manipulator using efficient modal control
Organized according to the steps in a control design project, the text first discusses kinematic and dynamic modeling methods, including programmed constraints, Lagrange's equations, Boltzmann-Hamel equations, and generalized programmed motion equations.
Model-Based Tracking Control of Nonlinear Systems
Dynamic behaviour analysis, respectively the writing of the piece movement governing equations with respect to a fixed coordinate system can be done based on analytical mechanics, namely, Lagrange's equations. As well as before, these feeding systems with disk having nests, respectively with rotor having horizontal palettes, can be considered particular types of one disk having inclined nests.
Mechatronic conception of feeding and dosing systems used in automat inspection systems
Using Lagrange's equations of the second kind (Ripianu, 1977), the differential equations for the TRT1 and RTT robots with three degrees of freedom were deduced, expressed by the equations (1) and (2).
The energy method of constructive optimization for the serial modular robots with three degrees of freedom
Next, Lagrange's equations are derived and their integration is discussed.
Analytical Dynamics: Theory and Applications
Copyright © 2003-2025 Farlex, Inc Disclaimer
All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.