Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 44, pp. 1-9.
Title: Non-monotone period functions for impact oscillators
Authors: Carmen Chicone (Univ. of Missouri-Columbia, MO, USA)
Kenny Felts (Univ. of Missouri-Columbia, MO, USA)
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.