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Journal of Applied Mathematics
Volume 2012, Article ID 268537, 34 pages
http://dx.doi.org/10.1155/2012/268537
Research Article

Towards a Prototype of a Spherical Tippe Top

1Howest, ELIT, University College West Flanders, G. K. De Goedelaan 5, 8500 Kortrijk, Belgium
2Department of Mathematical Analysis, Research Group NaM2, University of Ghent, Galglaan 2, 9000 Ghent, Belgium
3Department of Architecture, Sint-Lucas Visual Arts, Institute for Higher Education in the Sciences and the Arts, 9000 Ghent, Belgium
4Howest, Industrial Design Center, University College West Flanders, Marksesteenweg 58, 8500 Kortrijk, Belgium

Received 14 April 2011; Revised 6 October 2011; Accepted 7 October 2011

Academic Editor: Yuri Sotskov

Copyright © 2012 M. C. Ciocci et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Perry, Spinning Tops and Gyroscopic Motions, Dover, New York, NY, USA, 1957.
  2. C. M. Cohen, “The tippe top revisited,” American Journal of Physics, vol. 45, pp. 12–17, 1977. View at Publisher · View at Google Scholar
  3. C. G. Gray and B. G. Nickel, “Constants of the motion for nonslipping tippe tops and other tops with round pegs,” American Journal of Physics, vol. 68, no. 9, pp. 821–828, 2000. View at Publisher · View at Google Scholar
  4. A. C. Or, “The dynamics of a Tippe top,” SIAM Journal on Applied Mathematics, vol. 54, no. 3, pp. 597–609, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. N. M. Bou-Rabee, J. E. Marsden, and L. A. Romero, “Tippe top inversion as a dissipation-induced instability,” SIAM Journal on Applied Dynamical Systems, vol. 3, no. 3, pp. 352–377, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. E. J. Routh, Dynamics of a System of Rigid Bodies, MacMillan, New York, NY, USA, 1905.
  7. C. M. Braams, “On the influence of friction on the motion of a top,” Physica, vol. 18, pp. 503–514, 1952. View at Google Scholar · View at Zentralblatt MATH
  8. J. H. Jellett, A Treatise on the Theory of Friction, MacMillan, London, UK, 1872.
  9. T. R. Kane and D. Levinson, “A realistic solution of the symmetric top problem,” Journal of Applied Mechanics, vol. 45, pp. 903–909, 1978. View at Publisher · View at Google Scholar
  10. M. C. Ciocci and B. Langerock, “Dynamics of the tippe top via Routhian reduction,” International Journal of Bifurcation and Chaos, vol. 12, no. 6, pp. 602–614, 2007. View at Publisher · View at Google Scholar
  11. B. Y. M. Branicki, H. K. Moffatt, and Y. Shimomura, “Dynamics of an axisymmetric body spinning on a horizontal surface. III. Geometry of steady state structures for convex bodies,” Proceedings of the Royal Society of London. Series A, vol. 462, no. 2066, pp. 371–390, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. B. Y. M. Branicki and Y. Shimomura, “Dynamics of an axisymmetric body spinning on a horizontal surface. IV. Stability of steady spin states and the `rising egg' phenomenon for convex axisymmetric bodies,” Proceedings of the Royal Society of London. Series A, vol. 462, no. 2075, pp. 3253–3275, 2006. View at Publisher · View at Google Scholar
  13. S. Ebenfeld and F. Scheck, “A new analysis of the tippe top: asymptotic states and Liapunov stability,” Annals of Physics, vol. 243, no. 2, pp. 195–217, 1995. View at Publisher · View at Google Scholar
  14. S. Rauch-Wojciechowski, M. Sköldstam, and T. Glad, “Mathematical analysis of the tippe top,” Regular & Chaotic Dynamics, vol. 10, no. 4, pp. 333–362, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. H. K. Moffatt, Y. Shimomura, and M. Branicki, “Dynamics of an axisymmetric body spinning on a horizontal surface. I. Stability and the gyroscopic approximation,” Proceedings of The Royal Society of London. Series A, vol. 460, no. 2052, pp. 3643–3672, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. R. Bastiaens, J. Detand, O. Rysman, and T. Defloo, “Efficient use of traditional-, rapid- and virtual prototyping in the industrial product development process,” in Proceedings of the 3rd International Conference on Advanced Research in Virtual and Rapid Prototyping (VRAP '09), Lleira, Portugal, 2009. View at Publisher · View at Google Scholar
  17. V. I. Arnol’d, Dynamical Systems. Encyclopedia of Mathematical Sciences, vol. 3, Springer, New York, NY, USA, 1988. View at Zentralblatt MATH
  18. H. K. Moffatt and T. Tokieda, “Celt reversals: A prototype of chiral dynamics,” Proceedings of the Royal Society of Edinburgh Section A, vol. 138, no. 2, pp. 361–368, 2008. View at Publisher · View at Google Scholar
  19. T. Tokieda, “Private communications,” in Proceedings of the Geometric Mechanics and its Applications (MASIE), Lausanne, Switzerland, July 2004.
  20. C. Friedl, Der Stehoufkreisel, Zulassungsarbeit zum 1. Staatsexamen, Universität Augsburg, http://www.physik.uniaugsburg.de/%18wobsta/tippetop/index.shtml.en.
  21. T. Ueda, K. Sasaki, and S. Watanabe, “Motion of the tippe top: gyroscopic balance condition and stability,” SIAM Journal on Applied Dynamical Systems, vol. 4, no. 4, pp. 1159–1194, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH