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The practical use of variation principles in the determination of the stability of non linear systems

Published online by Cambridge University Press:  09 April 2009

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

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We are interested in the motion of non linear systems. In this paper we use a variation principle and an iteration procedure in order to treat the stability of free oscillations against small disturbances of the initial conditions. It is found that approximations to the low lying stability lines can be obtained using the Rayleigh-Ritz variation principle and that these approximations can be consistently improved using an iteration procedure. These approximations are compared with the tabulated values in the special case of the Mathieu Equation. The results are in general a considerable improvement on those obtained using the usual Perturbation Theory, and have a much wider range of validity.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 2 , Issue 2 , October 1961 , pp. 153 - 188
Copyright
Copyright © Australian Mathematical Society 1961

References

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