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Technical Briefs

Admissibility of Acceleration Dependent Forces in Newtonian Dynamics

[+] Author and Article Information
Amitabha Ghosh

Indian National Science Academy, New Delhi,  Bengal Engineering and Science University, Shibpur, Howrah, 711 103, India

J. Appl. Mech 79(4), 044501 (May 09, 2012) (3 pages) doi:10.1115/1.4005583 History: Received June 16, 2011; Revised November 13, 2011; Posted February 01, 2012; Published May 09, 2012; Online May 09, 2012

L. A. Pars (1964, A Treatise on Analytical Dynamics, Heinemann, London) has shown in his comprehensive treatise that acceleration dependent forces are not admissible in Newtonian mechanics. More recently, Zhechev (2007, On the Admissibility of Given Acceleration – Dependent Forces in Mechanics, Jr. of Applied Mechanics, ASME, 74 , Jan, pp. 107–111; 2007, Peculiarities of the use of Acceleration – Dependent Forces in Mechanical Problems, Proc. I. Mech. E, 221 Part K, pp. 497–503) has shown that the proof given by Pars is faulty and has concluded that acceleration dependent forces are admissible in Newtonian mechanics and in many cases such forces are useful in controlling mechanical systems. This brief technical note attempts to show that the matter is more complex and needs further discussion.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Interdependence of acceleration-dependent forces acting on a particle

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Figure 2

Possible motion(s) when an acceleration-dependent force acts on a particle

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Figure 3

Different situations with acceleration-dependent feed back force acting on a particle

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Figure 4

Representation of F = ma

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Figure 5

(a) Planes representing F = ma and a constant force; (b) motion characteristics for a constant applied force

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Figure 6

(a) Force depending upon both velocity and acceleration, (b) Motion characteristics for velocity and acceleration dependent force

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Figure 7

Permitted motion characteristics of a particle

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Figure 8

(a) Impossible type of velocity and acceleration dependence of force; (b) impossible situation in a motion characteristics resulting from a velocity and acceleration dependent force

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