Explicit Equations of Motion for Mechanical Systems With Nonideal ConstraintsSource: Journal of Applied Mechanics:;2001:;volume( 068 ):;issue: 003::page 462Author:F. E. Udwadia
,
Professor of Civil Engineering
,
Aerospace and Mechanical Engineering
,
R. E. Kalaba
,
Professor of Biomedical Engineering
,
Electrical Engineering
DOI: 10.1115/1.1364492Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Since its inception about 200 years ago, Lagrangian mechanics has been based upon the Principle of D’Alembert. There are, however, many physical situations where this confining principle is not suitable, and the constraint forces do work. To date, such situations are excluded from general Lagrangian formulations. This paper releases Lagrangian mechanics from this confinement, by generalizing D’Alembert’s principle, and presents the explicit equations of motion for constrained mechanical systems in which the constraints are nonideal. These equations lead to a simple and new fundamental view of Lagrangian mechanics. They provide a geometrical understanding of constrained motion, and they highlight the simplicity with which Nature seems to operate.
keyword(s): Force , Motion , Equations of motion , D'Alembert's principle AND Equations ,
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contributor author | F. E. Udwadia | |
contributor author | Professor of Civil Engineering | |
contributor author | Aerospace and Mechanical Engineering | |
contributor author | R. E. Kalaba | |
contributor author | Professor of Biomedical Engineering | |
contributor author | Electrical Engineering | |
date accessioned | 2017-05-09T00:04:02Z | |
date available | 2017-05-09T00:04:02Z | |
date copyright | May, 2001 | |
date issued | 2001 | |
identifier issn | 0021-8936 | |
identifier other | JAMCAV-26515#462_1.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/124704 | |
description abstract | Since its inception about 200 years ago, Lagrangian mechanics has been based upon the Principle of D’Alembert. There are, however, many physical situations where this confining principle is not suitable, and the constraint forces do work. To date, such situations are excluded from general Lagrangian formulations. This paper releases Lagrangian mechanics from this confinement, by generalizing D’Alembert’s principle, and presents the explicit equations of motion for constrained mechanical systems in which the constraints are nonideal. These equations lead to a simple and new fundamental view of Lagrangian mechanics. They provide a geometrical understanding of constrained motion, and they highlight the simplicity with which Nature seems to operate. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Explicit Equations of Motion for Mechanical Systems With Nonideal Constraints | |
type | Journal Paper | |
journal volume | 68 | |
journal issue | 3 | |
journal title | Journal of Applied Mechanics | |
identifier doi | 10.1115/1.1364492 | |
journal fristpage | 462 | |
journal lastpage | 467 | |
identifier eissn | 1528-9036 | |
keywords | Force | |
keywords | Motion | |
keywords | Equations of motion | |
keywords | D'Alembert's principle AND Equations | |
tree | Journal of Applied Mechanics:;2001:;volume( 068 ):;issue: 003 | |
contenttype | Fulltext |