Periodic orbits of an impact oscillator
Periodic orbits of an impact oscillator
An harmonically excited, undamped linear oscillator with impacts is considered. The structure of the orbit space for single-excitation-cycle, single impact periodic orbits is investigated, first for elastic and then for inelastic impacts. It is proved that these orbits form a smooth, connected three dimensional 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.
Harkness, Tom
f8add75b-93c3-4189-99ec-8ba73c6a6d8b
March 1999
Harkness, Tom
f8add75b-93c3-4189-99ec-8ba73c6a6d8b
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, single impact periodic orbits is investigated, first for elastic and then for inelastic impacts. It is proved that these orbits form a smooth, connected three dimensional 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
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University of Southampton
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Local EPrints ID: 50635
URI: http://eprints.soton.ac.uk/id/eprint/50635
PURE UUID: a24f8ce5-8e52-4fae-84aa-cf2134cceb33
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Date deposited: 06 Apr 2008
Last modified: 15 Mar 2024 10:09
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Author:
Tom Harkness
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