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Periodic orbits of an impact oscillator

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, 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.
Harkness, Tom
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Harkness, Tom
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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

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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: 13 Mar 2019 20:50

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