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The practical use of variation principles in non-linear mechanics

Published online by Cambridge University Press:  09 April 2009

J. M. Blatt  and
J. N. Lyness
J. M. Blatt
Affiliation:
Applied Mathematics Department, The University of New South Wales, Kensington, N.S.W., Australia.
J. N. Lyness
Affiliation:
Applied Mathematics Department, The University of New South Wales, Kensington, N.S.W., Australia.
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Abstract

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Contrary to the general impression that variation principles are of purely theoretical interest, we show by means of examples that they can lead to considerable practical advantages in the solution of non-linear vibration problems. In this paper, we develop a variation principle for the period of a free oscillation, as a function of the average value of the Lagrangian over one period. Even extremely simple-minded approximations to the true motion lead to excellent values for the period. The stability of such free oscillations against small disturbances of the initial conditions is treated in a previous paper.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 2 , Issue 3 , February 1962 , pp. 357 - 368
Copyright
Copyright © Australian Mathematical Society 1962

References

[1]Goldstein, H.: Classical Mechanics, Addison-Wesley Press, Cambridge, Mass., 1960.Google Scholar
[2]Lyness, J. N. and Blatt, J. M.: The Practical Use of Variation Principles in the Determination of the Stability of Non Linear Systems, J.A.M.S. Vol. II, Part. 2, 153, 1961Google Scholar
[3]Rosenberg, R. M. and Atkinson, C. P.: Journal of Appl. Mech., 3, 377, 1959.Google Scholar