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TECHNICAL BRIEFS

On the Extremal Properties of Hamilton’s Action Integral

[+] Author and Article Information
J. G. Papastavridis

School of Engineering Science and Mechanics, Georgia Institute of Technology, Atlanta, Ga. 30332

J. Appl. Mech 47(4), 955-956 (Dec 01, 1980) (2 pages) doi:10.1115/1.3153821 History: Received January 01, 1980; Revised June 01, 1980; Online July 21, 2009

Abstract

This Note examines the sufficient conditions for the extremization, in particular the minimization, of the action integral in Hamilton’s principle for a one-degree-of-freedom nonlinear conservative system. It is usually stated in analytical mechanics that the action is actually minimized only over a short-time interval. Here the quantification of these statements is achieved by obtaining an upper bound for this minimizing interval. This is attained by combining results from the sufficiency variational calculus theory, with oscillation/comparison theorems from differential equations.

Copyright © 1980 by ASME
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