Electron. J. Diff. Eqns., Vol. 2008(2008), No. 44, pp. 1-9.

Non-monotone period functions for impact oscillators

Carmen Chicone, Kenny Felts

Abstract:
The existence of non-monotone period functions for differential equations of the form
$$ \ddot{x}+f(x)+\gamma H(x)g(x)=0 $$
is proved for large $\gamma$, where H is the Heaviside function and the functions f and g satisfy certain generic conditions. This result is precipitated by an analysis of the system
$$ \ddot{x}+\sin x +\gamma H(x) x^{3/2}=0, $$
which models the conservative dimensionless impact pendulum utilizing Hertzian contact during impact with a barrier at the downward vertical position.

Submitted December 17, 2007. Published March 20, 2008.
Math Subject Classifications: 34C15, 34C25, 37N15.
Key Words: Period function; impact oscillator.

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Carmen Chicone
Department of Mathematics
University of Missouri-Columbia
Columbia, MO 65211-4100, USA
e-mail: carmen@chicone.math.missouri.edu
Kenny Felts
Department of Mathematics
University of Missouri-Columbia
Columbia MO 65211-4100, USA
email: krf835@mizzou.edu

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