{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T13:06:44Z","timestamp":1769000804198,"version":"3.49.0"},"reference-count":21,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,2,9]],"date-time":"2012-02-09T00:00:00Z","timestamp":1328745600000},"content-version":"vor","delay-in-days":39,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>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: <jats:italic>tipping, nontipping, hanging<\/jats:italic>, 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 \u201c3\u2010in\u20101 toy\u201d 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 \u201c<jats:italic>toy<\/jats:italic>\u201d is suitable to validate the mathematical model qualitatively and quantitatively.<\/jats:p>","DOI":"10.1155\/2012\/268537","type":"journal-article","created":{"date-parts":[[2012,2,9]],"date-time":"2012-02-09T21:03:01Z","timestamp":1328821381000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Towards a Prototype of a Spherical Tippe Top"],"prefix":"10.1155","volume":"2012","author":[{"given":"M. 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Efficient use of traditional- rapid- and virtual prototyping in the industrial product development process Proceedings of the 3rd International Conference on Advanced Research in Virtual and Rapid Prototyping (VRAP \u203209) 2009 Lleira Portugal https:\/\/doi.org\/10.1137\/030601351.","DOI":"10.1137\/030601351"},{"key":"e_1_2_10_17_2","volume-title":"Dynamical Systems. Encyclopedia of Mathematical Sciences","author":"Arnol\u2019d V. I.","year":"1988"},{"key":"e_1_2_10_18_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210506000679"},{"key":"e_1_2_10_19_2","unstructured":"TokiedaT. Private communications Proceedings of the Geometric Mechanics and its Applications (MASIE) July 2004 Lausanne Switzerland."},{"key":"e_1_2_10_20_2","unstructured":"FriedlC. Der Stehoufkreisel Zulassungsarbeit zum 1. Staatsexamen Universit\u00e4t Augsburg http:\/\/www.physik.uniaugsburg.de\/%18wobsta\/tippetop\/index.shtml.en."},{"key":"e_1_2_10_21_2","doi-asserted-by":"publisher","DOI":"10.1137\/040615985"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/268537.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/268537.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/268537","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:16:45Z","timestamp":1718090205000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/268537"}},"subtitle":[],"editor":[{"given":"Yuri","family":"Sotskov","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/268537"],"URL":"https:\/\/doi.org\/10.1155\/2012\/268537","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2011-04-14","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-10-07","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-02-09","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"268537"}}