On the Reciprocal Form of Hamilton’s Principle

[+] Author and Article Information
Z. M. Elias

Department of Civil Engineering, University of Washington, Seattle, Wash.

J. Appl. Mech 40(1), 93-100 (Mar 01, 1973) (8 pages) doi:10.1115/1.3422980 History: Received August 01, 1971; Revised March 01, 1972; Online July 12, 2010


A complementary energy principle for dynamic analysis due to Toupin is critically examined. It is found that the variational principle is a necessary but not a sufficient condition for geometric compatibility and that consequently it allows the occurrence of spurious solutions. A necessary and sufficient condition of compatibility is obtained through the reciprocal form of Hamilton’s principle which is derived for discrete and continuous systems. Additional terms appearing in the derived principle insure that spurious solutions cannot occur. The derived variational principle can be expressed in terms of stresses and velocities or in terms of impulses.

Copyright © 1973 by ASME
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