Hamilton's principle and the calculus of variations

Abstract

In the recent literature of the Calculus of variations, mathematical proofs have been presented for what the writers claim to be a more precise statement of Hamilton's Principle for conservative systems. Nothing is said about Hamilton's Principle for nonconservative systems. According to these writers, the action integral, the variation of which is Hamilton's Principle for conservative systems, is a minimum for discrete systems for small time intervals only and is never a minimum for continuous systems. The proof of this more precise statement is based in the sufficiency theorems of the Calculus of Variations. In this paper, two contradictions to the statement are demonstrated — one for a discrete system and one for a continuous system.