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.
Issue Section:
Research Papers
1.
Bolza
, O.
, 1931, Vorlesungen über Varationsrechnung
, Koehler und Amelang
, Leipzig
.2.
Douglas
, J.
, 1939, “Solution of the Inverse Problem of the Calculus of Variations
,” Proc. Natl. Acad. Sci. U.S.A.
0027-8424, 25
, pp. 631
–637
.3.
Douglas
, J.
, 1940, “Theorems in the Inverse Problem in the Calculus of Variations
,” Proc. Natl. Acad. Sci. U.S.A.
0027-8424, 26
, pp. 215
–221
.4.
Leitmann
, G.
, 1963, “Some Remarks on Hamilton’s Principle
,” ASME J. Appl. Mech.
0021-8936, 30
, pp. 623
–625
.5.
He
, J. -H.
, 2004, “Variational Principles for Some Nonlinear Partial Differential Equations With Variable Coefficients
,” Chaos, Solitons Fractals
0960-0779, 19
, pp. 847
–851
.6.
Leitmann
, G.
, 1986, The Calculus of Variations and Optimal Control: An Introduction
, Springer
, New York
.7.
Musielak
, Z. E.
, 2008, “Standard and Non-Standard Lagrangians for Dissipative Dynamical Systems With Variable Coefficients
,” J. Phys. A: Math. Theor.
1751-8113, 41
, p. 055205
.Copyright © 2011
by American Society of Mechanical Engineers
You do not currently have access to this content.
