Some Further Remarks on Hamilton's Principle

[en] This paper deals with the inverse problem of finding a suitable integrand so that upon the use of the calculus of variations, one obtains the equations of motion for systems in which the forces are nonpotential. New extensions and generalizations of previous results are obtained.

Disciplines :

Mechanical engineering

Author, co-author :

Udwadia, Firdaus; University of Southern California > Department of Aerospace and Mechanical Engineering

Leitmann, George; Berkeley University of California - UC Berkeley > Department of Mechanical Engineering

Cho, Hancheol ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Language :

English

Title :

Some Further Remarks on Hamilton's Principle

Publication date :

2011

Journal title :

Journal of Applied Mechanics

ISSN :

0021-8936

eISSN :

1528-9036

Publisher :

American Society of Mechanical Engineers, New York, United States - New York

Volume :

Issue :

Pages :

011014-1 – 011014-4

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 20 January 2016

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Bibliography

Bolza, O., 1931, Vorlesungen über Varationsrechnung, Koehler und Amelang, Leipzig.
Douglas, J., 1939, "Solution of the Inverse Problem of the Calculus of Variations", Proc. Natl. Acad. Sci. U. S. A., 25, pp. 631-637.
Douglas, J., 1940, "Theorems in the Inverse Problem in the Calculus of Variations", Proc. Natl. Acad. Sci. U. S. A., 26, pp. 215-221.
Leitmann, G., 1963, "Some Remarks on Hamilton's Principle", ASME J. Appl. Mech., 30, pp. 623-625.
He, J.-H., 2004, "Variational Principles for Some Nonlinear Partial Differential Equations With Variable Coefficients", Chaos, Solitons Fractals, 19, pp. 847-851.
Leitmann, G., 1986, The Calculus of Variations and Optimal Control: An Introduction, Springer, New York.
Musielak, Z. E., 2008, "Standard and Non-Standard Lagrangians for Dissipative Dynamical Systems With Variable Coefficients", J. Phys. A: Math. Theor., 41, p. 055205.