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Dynamics of the tippe top via Routhian reduction

(2007) REGULAR & CHAOTIC DYNAMICS. 12(6). p.602-614
Author
Organization
Abstract
We consider a tippe top modeled as an eccentric sphere, spinning on a horizontal table and subject to a sliding friction. Ignoring translational effects, we show that the system is reducible using a Routhian reduction technique. The reduced system is a two dimensional system of second order differential equations, that allows an elegant and compact way to retrieve the classification of tippe tops in six groups as proposed in [1] according to the existence and stability type of the steady states.
Keywords
bifurcation, STABILITY, (linear) stability, relative equilibria, Routhian reduction, symmetries, Lagrangian equations, tippe top, eccentric sphere, MOTION

Citation

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Chicago
Ciocci, Maria-Cristina, and B Langerock. 2007. “Dynamics of the Tippe Top via Routhian Reduction.” Regular & Chaotic Dynamics 12 (6): 602–614.
APA
Ciocci, M.-C., & Langerock, B. (2007). Dynamics of the tippe top via Routhian reduction. REGULAR & CHAOTIC DYNAMICS, 12(6), 602–614.
Vancouver
1.
Ciocci M-C, Langerock B. Dynamics of the tippe top via Routhian reduction. REGULAR & CHAOTIC DYNAMICS. 2007;12(6):602–14.
MLA
Ciocci, Maria-Cristina, and B Langerock. “Dynamics of the Tippe Top via Routhian Reduction.” REGULAR & CHAOTIC DYNAMICS 12.6 (2007): 602–614. Print.
@article{1200758,
  abstract     = {We consider a tippe top modeled as an eccentric sphere, spinning on a horizontal table and subject to a sliding friction. Ignoring translational effects, we show that the system is reducible using a Routhian reduction technique. The reduced system is a two dimensional system of second order differential equations, that allows an elegant and compact way to retrieve the classification of tippe tops in six groups as proposed in [1] according to the existence and stability type of the steady states.},
  author       = {Ciocci, Maria-Cristina and Langerock, B},
  issn         = {1560-3547},
  journal      = {REGULAR \& CHAOTIC DYNAMICS},
  keyword      = {bifurcation,STABILITY,(linear) stability,relative equilibria,Routhian reduction,symmetries,Lagrangian equations,tippe top,eccentric sphere,MOTION},
  language     = {eng},
  number       = {6},
  pages        = {602--614},
  title        = {Dynamics of the tippe top via Routhian reduction},
  url          = {http://dx.doi.org/10.1134/S1560354707060032},
  volume       = {12},
  year         = {2007},
}

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