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A prototype of a spherical tippe top

Cristina Ciocci UGent, Benny Malengier UGent and Bart Grimonprez UGent (2012) Innovative developments in virtual and physical prototyping. p.157-162
abstract
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. It is the friction with the bottom surface and the position of the center of mass below the centre of curvature that cause the tippe top to rise its centre of mass while continuing rotating around its symmetry axis (through 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. According to the eccentricity of the sphere and the Jellet invariant (which includes information on the initial angular velocity) three main different dynamical behaviours are distinguished: tipping, non-tipping, hanging (i.e. 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 quantitative verification of the mathematical model. We applied 3D-printing 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. This 'toy' allows verification by experimentation.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
keyword
DYNAMICS, STABILITY
in
Innovative developments in virtual and physical prototyping
editor
PJ Bartolo, ACS DeLemos, APO Tojeira, AMH Pereira, AJ Mateus, ALA Mendes, C DosSantos, DMF Freitas, HM Bartolo, HD Almeida, IM DosReis, JR Dias, MAN Domingos, NMF Alves, RFB Pereira, TMF Patricio and Telma Margarida Dias Ferreira
pages
157 - 162
publisher
CRC Press
place of publication
Boca Raton, FL, USA
conference name
5th International conference on Advanced Research in Virtual and Rapid Prototyping (VRAP 2011)
conference location
Leira, Portugal
conference start
2011-09-28
conference end
2011-10-01
Web of Science type
Proceedings Paper
Web of Science id
000305445600023
ISBN
9780415684187
9780203181416
DOI
10.1201/b11341-27
language
English
UGent publication?
yes
classification
P1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2048223
handle
http://hdl.handle.net/1854/LU-2048223
date created
2012-02-28 10:43:25
date last changed
2015-06-17 09:58:27
@inproceedings{2048223,
  abstract     = {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. It is the friction with the bottom surface and the position of the center of mass below the centre of curvature that cause the tippe top to rise its centre of mass while continuing rotating around its symmetry axis (through 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. According to the eccentricity of the sphere and the Jellet invariant (which includes information on the initial angular velocity) three main different dynamical behaviours are distinguished: tipping, non-tipping, hanging (i.e. 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 quantitative verification of the mathematical model. We applied 3D-printing 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. This 'toy' allows verification by experimentation.},
  author       = {Ciocci, Cristina and Malengier, Benny and Grimonprez, Bart},
  booktitle    = {Innovative developments in virtual and physical prototyping},
  editor       = {Bartolo, PJ and DeLemos, ACS and Tojeira, APO and Pereira, AMH and Mateus, AJ and Mendes, ALA and DosSantos, C and Freitas, DMF and Bartolo, HM and Almeida, HD and DosReis, IM and Dias, JR and Domingos, MAN and Alves, NMF and Pereira, RFB and Patricio, TMF and Dias Ferreira, Telma Margarida},
  isbn         = {9780415684187},
  keyword      = {DYNAMICS,STABILITY},
  language     = {eng},
  location     = {Leira, Portugal},
  pages        = {157--162},
  publisher    = {CRC Press},
  title        = {A prototype of a spherical tippe top},
  url          = {http://dx.doi.org/10.1201/b11341-27},
  year         = {2012},
}

Chicago
Ciocci, Cristina, Benny Malengier, and Bart Grimonprez. 2012. “A Prototype of a Spherical Tippe Top.” In Innovative Developments in Virtual and Physical Prototyping, ed. PJ Bartolo, ACS DeLemos, APO Tojeira, AMH Pereira, AJ Mateus, ALA Mendes, C DosSantos, et al., 157–162. Boca Raton, FL, USA: CRC Press.
APA
Ciocci, C., Malengier, B., & Grimonprez, B. (2012). A prototype of a spherical tippe top. In PJ Bartolo, A. DeLemos, A. Tojeira, A. Pereira, A. Mateus, A. Mendes, C. DosSantos, et al. (Eds.), Innovative developments in virtual and physical prototyping (pp. 157–162). Presented at the 5th International conference on Advanced Research in Virtual and Rapid Prototyping (VRAP 2011), Boca Raton, FL, USA: CRC Press.
Vancouver
1.
Ciocci C, Malengier B, Grimonprez B. A prototype of a spherical tippe top. In: Bartolo P, DeLemos A, Tojeira A, Pereira A, Mateus A, Mendes A, et al., editors. Innovative developments in virtual and physical prototyping. Boca Raton, FL, USA: CRC Press; 2012. p. 157–62.
MLA
Ciocci, Cristina, Benny Malengier, and Bart Grimonprez. “A Prototype of a Spherical Tippe Top.” Innovative Developments in Virtual and Physical Prototyping. Ed. PJ Bartolo et al. Boca Raton, FL, USA: CRC Press, 2012. 157–162. Print.