Admissibility of Acceleration Dependent Forces in Newtonian Dynamics

Abstract

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.