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Periodic orbits of an impact oscillator

Harkness, Tom (1999) Periodic orbits of an impact oscillator. University of Southampton, Department of Mathematics, Doctoral Thesis, 212pp.

Record type: Thesis (Doctoral)

Abstract

An harmonically excited, undamped linear oscillator with impacts is considered. The structure of the orbit space for single-excitation-cycle, singleimpact periodic orbits is investigated, first for elastic and then for inelastic impacts. It is proved that these orbits form a smooth, connected threedimensional manifold in the five-dimensional global parameter space. A study of the dynamic stability of these orbits then shows that the linearly stable region occupies an open submanifold. Numerically generated diagrams representing projections of the orbit spaces for a range of restitution coefficients are included. In addition, the impact surface — a representation in phase space of the impact obstacle — is explored and some new results on its variation with respect to the position of the obstacle are presented.

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Published date: March 1999
Organisations: University of Southampton

Identifiers

Local EPrints ID: 50635
URI: http://eprints.soton.ac.uk/id/eprint/50635
PURE UUID: a24f8ce5-8e52-4fae-84aa-cf2134cceb33

Catalogue record

Date deposited: 06 Apr 2008

Contributors

Author: Tom Harkness