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TECHNICAL BRIEFS

On the Sufficiency of the Principle of Virtual Work for Mechanical Equilibrium: A Critical Reexamination

[+] Author and Article Information
John G. Papastavridis

School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

J. Appl. Mech 56(3), 704-707 (Sep 01, 1989) (4 pages) doi:10.1115/1.3176150 History: Received July 29, 1988; Revised October 26, 1988; Online July 21, 2009

Abstract

Starting from the general kinetic principle of d’Alembert/Lagrange, an energetic proof of the sufficiency conditions for equilibrium (known as Principle of Virtual Work) is presented. It is clearly demonstrated why to maintain equilibrium requires that, in addition to the familiar vanishing of the virtual work of the impressed forces on the originally motionless system, its geometrical (holonomic) constraints be explicitly time independent (stationary) and its nonintegrable kinematical (nonholonomic) ones be linear and homogeneous in the generalized velocities (catastatic).

Copyright © 1989 by ASME
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