Towards a Prototype of a Spherical Tippe Top
Among spinning objects, the tippe top exhibits one of the most bizarre and counterintuitive behaviours. The commercially available tippe tops basically consist of a section of a sphere with a rod. After spinning on its rounded body, the top flips over and continues spinning on the stem. The commonly...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/268537 |
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| _version_ | 1832548894540562432 |
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| author | M. C. Ciocci B. Malengier B. Langerock B. Grimonprez |
| author_facet | M. C. Ciocci B. Malengier B. Langerock B. Grimonprez |
| author_sort | M. C. Ciocci |
| collection | DOAJ |
| description | Among spinning objects, the tippe top exhibits one of the most bizarre and counterintuitive behaviours. The commercially available tippe tops basically consist of a section of a sphere with a rod. After spinning on its rounded body, the top flips over and continues spinning on the stem. The commonly used simplified mathematical model for the tippe top is a sphere whose mass distribution is axially but not spherically symmetric, spinning on a flat surface subject to a small friction force that is due to sliding. Three main different dynamical behaviours are distinguished: tipping, nontipping, hanging, that is, the top rises but converges to an intermediate state instead of rising all the way to the vertical state. Subclasses according to the stability of relative equilibria can further be distinguished. Our concern is the degree of confidence in the mathematical model predictions, we applied 3D printing and rapid prototyping to manufacture a “3-in-1 toy” that could catch the three main characteristics defining the three main groups in the classification of spherical tippe tops as mentioned above. We propose three designs. This “toy” is suitable to validate the mathematical model qualitatively and quantitatively. |
| format | Article |
| id | doaj-art-7d364ec50956496d922cb8c518ae41ae |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-7d364ec50956496d922cb8c518ae41ae2025-02-03T06:12:45ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/268537268537Towards a Prototype of a Spherical Tippe TopM. C. Ciocci0B. Malengier1B. Langerock2B. Grimonprez3Howest, ELIT, University College West Flanders, G. K. De Goedelaan 5, 8500 Kortrijk, BelgiumDepartment of Mathematical Analysis, Research Group NaM2, University of Ghent, Galglaan 2, 9000 Ghent, BelgiumDepartment of Architecture, Sint-Lucas Visual Arts, Institute for Higher Education in the Sciences and the Arts, 9000 Ghent, BelgiumHowest, Industrial Design Center, University College West Flanders, Marksesteenweg 58, 8500 Kortrijk, BelgiumAmong spinning objects, the tippe top exhibits one of the most bizarre and counterintuitive behaviours. The commercially available tippe tops basically consist of a section of a sphere with a rod. After spinning on its rounded body, the top flips over and continues spinning on the stem. The commonly used simplified mathematical model for the tippe top is a sphere whose mass distribution is axially but not spherically symmetric, spinning on a flat surface subject to a small friction force that is due to sliding. Three main different dynamical behaviours are distinguished: tipping, nontipping, hanging, that is, the top rises but converges to an intermediate state instead of rising all the way to the vertical state. Subclasses according to the stability of relative equilibria can further be distinguished. Our concern is the degree of confidence in the mathematical model predictions, we applied 3D printing and rapid prototyping to manufacture a “3-in-1 toy” that could catch the three main characteristics defining the three main groups in the classification of spherical tippe tops as mentioned above. We propose three designs. This “toy” is suitable to validate the mathematical model qualitatively and quantitatively.http://dx.doi.org/10.1155/2012/268537 |
| spellingShingle | M. C. Ciocci B. Malengier B. Langerock B. Grimonprez Towards a Prototype of a Spherical Tippe Top Journal of Applied Mathematics |
| title | Towards a Prototype of a Spherical Tippe Top |
| title_full | Towards a Prototype of a Spherical Tippe Top |
| title_fullStr | Towards a Prototype of a Spherical Tippe Top |
| title_full_unstemmed | Towards a Prototype of a Spherical Tippe Top |
| title_short | Towards a Prototype of a Spherical Tippe Top |
| title_sort | towards a prototype of a spherical tippe top |
| url | http://dx.doi.org/10.1155/2012/268537 |
| work_keys_str_mv | AT mcciocci towardsaprototypeofasphericaltippetop AT bmalengier towardsaprototypeofasphericaltippetop AT blangerock towardsaprototypeofasphericaltippetop AT bgrimonprez towardsaprototypeofasphericaltippetop |