Numerical Study of the Elastic Pendulum on the Rotating EarthReport as inadecuate




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ISRN Mathematical PhysicsVolume 2012 2012, Article ID 806231, 7 pages

Research Article

Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000 Ljubljana, Slovenia

Department of Experimental Particle Physics, Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia

Received 16 September 2011; Accepted 16 October 2011

Academic Editor: G. Cleaver

Copyright © 2012 Aleš Stanovnik and Borut Jurčič-Zlobec. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The elastic pendulum is a simple physical system represented by nonlinear differential equations. Analytical solutions for the bob trajectories on the rotating earth may be obtained in two limiting cases: for the ideally elastic pendulum with zero unstressed string length and for the Foucault pendulum with an inextensible string. The precession period of the oscillation plane, as seen by the local observer on the rotating earth, is 24 hours in the first case and has a well-known latitude dependence in the second case. In the present work, we have obtained numerical solutions of the nonlinear equations for different string elasticities in order to study the transition from one precession period to the other. It is found that the transition is abrupt and that it occurs for a quite small perturbation of the ideally elastic pendulum, that is, for the unstressed string length equal to about 10

of the equilibrium length due to theweight of the bob.





Author: Aleš Stanovnik and Borut Jurčič-Zlobec

Source: https://www.hindawi.com/



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