Publications on the Swinging Spring
The first substantive study of this system was by Vitt and Gorelik.
Their paper, originally published in Russian in 1933 has been translated and
published by Met Éireann as a Historical Note:
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Vitt, A and G Gorelik, 1933: Oscillations of an Elastic Pendulum as an Example of the
Oscillations of Two Parametrically Coupled Linear Systems. Translated by Lisa Shields,
with an Introduction by Peter Lynch.
Historical Note No. 3, Met Éireann, Dublin (1999).
Introduction and Abstract (HTML).
Report available as a
PDF file.
For further discussion on the elastic pendulum, the following may be of interest:
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Lynch, Peter, 2002:
Resonant Motions of the Three-dimensional Elastic Pendulum.
PDF file.
J. Nonlin. Mech, 37, 345-367.
Abstract (HTML).
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Lynch, Peter, 2002:
The Swinging Spring: a Simple Model for Atmospheric Balance.
PDF file.
In Proceedings of the Symposium on the Mathematics of
Atmosphere-Ocean Dynamics.
Isaac Newton Institute, June-December, 1996. Cambridge University Press.
Abstract (HTML).
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Holm, Darryl D. and Peter Lynch, 2002:
Stepwise Precession of the Resonant Swinging Spring.
PDF file.
SIAM Journal on Applied Dynamical Systems,
1, 44-64.
Abstract (HTML).
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Lynch, Peter, and Conor Houghton, 2003:
and Precession of the Resonant Swinging Spring .
PDF file.
Submitted to Physica D.
Abstract (HTML).
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Updated March 15th, 2003.