Comment on "Application of Hamilton's Law of Varying Action"

Abstract

I N a recent Comment on our paper, Professor Bailey made several statements to which we responded in our Reply. That Reply closed with the remark that further comment on Professor Bailey's procedure would be more appropriate at another time in another place; now is the time, and this is the place. Many of the concepts in Ref. 1 are repeated in Ref. 4, so that of necessity some of our statements in Ref. 3 will be repeated in this Comment. Professor Bailey's Eq. (3) in Ref. 4 is an incorrect statement of Hamilton's principle for general application. Just below that equation, one reads that it is understood that Wis the work of both conservative and nonconservative forces, and then Eq. (12) purports to offer a work function when there exist dissipative forces and time dependent forces. This is wrong. By definition, a work function does not exist for nonconservative systems since a work function is conventionally merely the negative of the potential energy, and potentials do not exist for nonconservative forces. There are internal inconsistencies between Eq. (2), Eq. (12), and what is actually used to get the numerical results of Figs. 3 and 4. Assume that WW(qh qt) as shown in Eq. (12). Then Eq. (2) implies that