On the Admissibility of Given Acceleration-Dependent Forces in Mechanics

[+] Author and Article Information
Michael M. Zhechev

Department of Vehicle Statistical Dynamics,  Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the National Space Agency of Ukraine, 15 Leshko-Popel Street, Dniepropetrovsk 49005, Ukrainezhechev@optima.com.ua

J. Appl. Mech 74(1), 107-110 (Dec 15, 2005) (4 pages) doi:10.1115/1.2187528 History: Received November 10, 2004; Revised December 15, 2005

In his book “A Treatise on Analytical Dynamics,” Pars asserted that acceleration-dependent forces are inconsistent with one of the fundamental principles of mechanics, namely, with the superposition principle, thus spreading among mechanical scientists the idea that such forces are not admissible in mechanics. This article demonstrates that given forces that depend on acceleration or higher derivatives are admissible in mechanics and shows that this assertion in Pars’s book is fallacious and the only condition for the applicability of such forces is the equation of motion possessing a unique solution.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Particle acted on by two forces; (a) acceleration-dependent forces (illustration to Pars’s proof), (b) opposing forces equal in magnitude, (c) interrelated forces (F1+F2=1N), (d) particle resting on an immovable support



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