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SIGMA, 2012, Volume 8, 019, 22 pages (Mi sigma696)  

This article is cited in 3 scientific papers (total in 3 papers)

Tippe Top equations and equations for the related mechanical systems

Nils Rutstam

Department of Mathematics, Linköping University, Linköping, Sweden

Abstract: The equations of motion for the rolling and gliding Tippe Top (TT) are nonintegrable and difficult to analyze. The only existing arguments about TT inversion are based on analysis of stability of asymptotic solutions and the LaSalle type theorem. They do not explain the dynamics of inversion. To approach this problem we review and analyze here the equations of motion for the rolling and gliding TT in three equivalent forms, each one providing different bits of information about motion of TT. They lead to the main equation for the TT, which describes well the oscillatory character of motion of the symmetry axis $\mathbf{\hat{3}}$ during the inversion. We show also that the equations of motion of TT give rise to equations of motion for two other simpler mechanical systems: the gliding heavy symmetric top and the gliding eccentric cylinder. These systems can be of aid in understanding the dynamics of the inverting TT.

Keywords: tippe top, rigid body, nonholonomic mechanics, integrals of motion, stability, gliding friction.

DOI: https://doi.org/10.3842/SIGMA.2012.019

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Full text: http://emis.mi.ras.ru/.../019
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Bibliographic databases:

ArXiv: 1204.1123
MSC: 70F40; 74M10; 70E18; 70E40; 37B25
Received: October 21, 2011; in final form March 27, 2012; Published online April 5, 2012
Language:

Citation: Nils Rutstam, “Tippe Top equations and equations for the related mechanical systems”, SIGMA, 8 (2012), 019, 22 pp.

Citation in format AMSBIB
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\by Nils Rutstam
\paper Tippe Top equations and equations for the related mechanical systems
\jour SIGMA
\yr 2012
\vol 8
\papernumber 019
\totalpages 22
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\crossref{https://doi.org/10.3842/SIGMA.2012.019}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84859553312}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Stefan Rauch-Wojciechowski, Nils Rutstam, “Dynamics of the Tippe Top Properties of Numerical Solutions Versus the Dynamical Equations”, Regul. Chaotic Dyn., 18:4 (2013), 453–467  mathnet  crossref  mathscinet  zmath
    2. Nils Rutstam, “High Frequency Behavior of a Rolling Ball and Simplification of the Separation Equation”, Regul. Chaotic Dyn., 18:3 (2013), 226–236  mathnet  crossref  mathscinet  zmath
    3. Stefan Rauch-Wojciechowski, Nils Rutstam, “Dynamics of an Inverting Tippe Top”, SIGMA, 10 (2014), 017, 18 pp.  mathnet  crossref  mathscinet
  • Symmetry, Integrability and Geometry: Methods and Applications
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