On the existence of periodic and eventually periodic solutions of a fluid dynamic forced harmonic oscillator

For certain flow regimes, the nonlinear differential equation Y¨=F(Y)−G, Y≥0, G>0 and constant, models qualitatively the behaviour of a forced, fluid dynamic, harmonic oscillator which has been a popular department store attraction. The device consists of a ball oscillating suspended in the verti...

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Bibliographic Details
Main Author:	Charlie H. Cooke
Format:	Article
Language:	English
Published:	Hindawi Limited 1986-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	nonlinear fluid dynamics forced harmonic oscillator eventually periodic motion sets of attraction.
Online Access:	http://dx.doi.org/10.1155/S0161171286000479

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spelling	doaj-eec6d35b390949c28d9b636ba2857d902020-11-24T23:44:15ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019238138510.1155/S0161171286000479On the existence of periodic and eventually periodic solutions of a fluid dynamic forced harmonic oscillatorCharlie H. Cooke0Department of Mathematical Sciences, Old Dominion University, Norfolk 23508, Virginia, USAFor certain flow regimes, the nonlinear differential equation Y¨=F(Y)−G, Y≥0, G>0 and constant, models qualitatively the behaviour of a forced, fluid dynamic, harmonic oscillator which has been a popular department store attraction. The device consists of a ball oscillating suspended in the vertical jet from a household fan. From the postulated form of the model, we determine sets of attraction and exploit symmetry properties of the system to show that all solutions are either initially periodic, with the ball never striking the fan, or else eventually approach a periodic limit cycle, after a sufficient number of bounces away from the fan.http://dx.doi.org/10.1155/S0161171286000479nonlinear fluid dynamicsforced harmonic oscillatoreventually periodic motionsets of attraction.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Charlie H. Cooke
spellingShingle	Charlie H. Cooke On the existence of periodic and eventually periodic solutions of a fluid dynamic forced harmonic oscillator International Journal of Mathematics and Mathematical Sciences nonlinear fluid dynamics forced harmonic oscillator eventually periodic motion sets of attraction.
author_facet	Charlie H. Cooke
author_sort	Charlie H. Cooke
title	On the existence of periodic and eventually periodic solutions of a fluid dynamic forced harmonic oscillator
title_short	On the existence of periodic and eventually periodic solutions of a fluid dynamic forced harmonic oscillator
title_full	On the existence of periodic and eventually periodic solutions of a fluid dynamic forced harmonic oscillator
title_fullStr	On the existence of periodic and eventually periodic solutions of a fluid dynamic forced harmonic oscillator
title_full_unstemmed	On the existence of periodic and eventually periodic solutions of a fluid dynamic forced harmonic oscillator
title_sort	on the existence of periodic and eventually periodic solutions of a fluid dynamic forced harmonic oscillator
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1986-01-01
description	For certain flow regimes, the nonlinear differential equation Y¨=F(Y)−G, Y≥0, G>0 and constant, models qualitatively the behaviour of a forced, fluid dynamic, harmonic oscillator which has been a popular department store attraction. The device consists of a ball oscillating suspended in the vertical jet from a household fan. From the postulated form of the model, we determine sets of attraction and exploit symmetry properties of the system to show that all solutions are either initially periodic, with the ball never striking the fan, or else eventually approach a periodic limit cycle, after a sufficient number of bounces away from the fan.
topic	nonlinear fluid dynamics forced harmonic oscillator eventually periodic motion sets of attraction.
url	http://dx.doi.org/10.1155/S0161171286000479
work_keys_str_mv	AT charliehcooke ontheexistenceofperiodicandeventuallyperiodicsolutionsofafluiddynamicforcedharmonicoscillator
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On the existence of periodic and eventually periodic solutions of a fluid dynamic forced harmonic oscillator

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