Chaotic Behavior of the Biharmonic Dynamics System

Motion of a biharmonic system under action of small periodic force and small damped force is studied. The biharmonic oscillator is a physical system acting under a biharmonic force like asin⁡θ+bsin⁡2θ. The article contains biharmonic oscillator analysis, phase space research, and analytic solutions...

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Main Author:	Vladimir S. Aslanov
Format:	Article
Language:	English
Published:	Hindawi Limited 2009-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Online Access:	http://dx.doi.org/10.1155/2009/319179

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spelling	doaj-aea225592b55481aba65df66206ba4112020-11-24T21:04:30ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/319179319179Chaotic Behavior of the Biharmonic Dynamics SystemVladimir S. Aslanov0Theoretical Mechanics Department, Faculty of Aircraft Construction, Samara State Aerospace University (SSAU), 34 Moscovskoe shosse, 443086 Samara, RussiaMotion of a biharmonic system under action of small periodic force and small damped force is studied. The biharmonic oscillator is a physical system acting under a biharmonic force like asin⁡θ+bsin⁡2θ. The article contains biharmonic oscillator analysis, phase space research, and analytic solutions for separatrixes. The biharmonic oscillator performs chaotic motion near separatrixes under small perturbations. Melnikov method gives analytical criterion for heteroclinic chaos in terms of system parameters. A transition from chaotic to regular motion of the biharmonic oscillator was found as the heteroclinic chaos can be removed by increasing the coefficient of a damping force. The analytical results obtained using Melnikov method have been confirmed by a good match with numeric research.http://dx.doi.org/10.1155/2009/319179
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Vladimir S. Aslanov
spellingShingle	Vladimir S. Aslanov Chaotic Behavior of the Biharmonic Dynamics System International Journal of Mathematics and Mathematical Sciences
author_facet	Vladimir S. Aslanov
author_sort	Vladimir S. Aslanov
title	Chaotic Behavior of the Biharmonic Dynamics System
title_short	Chaotic Behavior of the Biharmonic Dynamics System
title_full	Chaotic Behavior of the Biharmonic Dynamics System
title_fullStr	Chaotic Behavior of the Biharmonic Dynamics System
title_full_unstemmed	Chaotic Behavior of the Biharmonic Dynamics System
title_sort	chaotic behavior of the biharmonic dynamics system
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	2009-01-01
description	Motion of a biharmonic system under action of small periodic force and small damped force is studied. The biharmonic oscillator is a physical system acting under a biharmonic force like asin⁡θ+bsin⁡2θ. The article contains biharmonic oscillator analysis, phase space research, and analytic solutions for separatrixes. The biharmonic oscillator performs chaotic motion near separatrixes under small perturbations. Melnikov method gives analytical criterion for heteroclinic chaos in terms of system parameters. A transition from chaotic to regular motion of the biharmonic oscillator was found as the heteroclinic chaos can be removed by increasing the coefficient of a damping force. The analytical results obtained using Melnikov method have been confirmed by a good match with numeric research.
url	http://dx.doi.org/10.1155/2009/319179
work_keys_str_mv	AT vladimirsaslanov chaoticbehaviorofthebiharmonicdynamicssystem
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Chaotic Behavior of the Biharmonic Dynamics System

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