Feedback linearization of shimmy

Gabor Stepan, Bill Goodwine

Research output: Contribution to conferencePaper

1 Citation (Scopus)


Many vehicle systems contain rolling elements which exhibit unstable rolling motion, called shimmying, which may lead to disastrous results. The classical shimmying wheel is a simple model which captures the essential dynamics of such systems. In particular, the uncontrolled stability of the rolling wheel is characterized by a subcritical Hopf bifurcation when certain parameter values are varied. As such, the equilibrium state for the system may be unstable, and even if it is stable, sufficiently non-local initial conditions will lead to unstable dynamics. To control this unstable behavior, a particular geometric structure of this model can be exploited which provides a simple means to design a globally stabilizing controller by the means of feedback linearization.

Original languageEnglish
Number of pages8
Publication statusPublished - Dec 1 1998


ASJC Scopus subject areas

  • Engineering(all)

Cite this

Stepan, G., & Goodwine, B. (1998). Feedback linearization of shimmy. 429-436.