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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| Format: | Article |
| Language: | English |
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Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171286000479 |
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| _version_ | 1850162969382486016 |
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| author | Charlie H. Cooke |
| author_facet | Charlie H. Cooke |
| author_sort | Charlie H. Cooke |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-eec6d35b390949c28d9b636ba2857d90 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-eec6d35b390949c28d9b636ba2857d902025-08-20T02:22:25ZengWileyInternational 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. |
| 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. |
| title | 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_short | 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 |
| 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 |