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On the application of a numerical algorithm for Hopf bifuraction to the hunting of a wheelset

Published online by Cambridge University Press:  17 February 2009

R. R. Huilgol ,
R. Janus ,
M. A. Lohe  and
T. W. Sag
T. W. Sag
Affiliation:
School of Mathematical Sciences, Flinders University of South Australia, Bedford Park, S.A. 5042.
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Abstract

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The main ideas of Hopf bifurcation theory and its relevance to the development of periodic motions of an autonomous system depending on a parameter are presented, and an algorithm for the computation of the orbits is described. It is then shown that a model system for the motion of a wheelset can be cast in the form amenable to Hopf bifurcation theory. Numerical results for the period and amplitudes of the lateral and yaw motions are obtained in terms of the forward speed of the wheelset, and the wheel-rail profile parameters.

It is found that the period of oscillation decreases while the lateral and yaw motion amplitudes increase as the forward speed increases, for any given rail and wheel profile. While the effect of wheel curvature on the lateral motions seems to be non-existent, its effect on the yaw motion amplitude and the period is to increase them very slightly as the wheel profile changes from a conical to a curved profile. On the other hand, the effect of rail curvature on the lateral amplitude, for instance, is significant; the larger the curvature the smaller the amplitude for a given forward speed.

Type
Research Article
Information
The ANZIAM Journal , Volume 25 , Issue 3 , January 1984 , pp. 384 - 405
Copyright
Copyright © Australian Mathematical Society 1984

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