Abstract:
We study the relationship between numerical solutions for inverting Tippe Top and the structure of the dynamical equations. The numerical solutions confirm the oscillatory behavior of the inclination angle $\theta(t)$ for the symmetry axis of the Tippe Top, as predicted by the Main Equation for the Tippe Top. They also reveal further fine features of the dynamics of inverting solutions defining the time of inversion. These features are partially understood on the basis of the underlying dynamical equations.
Citation:
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
\Bibitem{RauRut13}
\by Stefan Rauch-Wojciechowski, Nils Rutstam
\paper Dynamics of the Tippe Top — Properties of Numerical Solutions Versus the Dynamical Equations
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 4
\pages 453--467
\mathnet{http://mi.mathnet.ru/rcd122}
\crossref{https://doi.org/10.1134/S1560354713040084}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3090211}
\zmath{https://zbmath.org/?q=an:1274.70018}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000322878100008}
Linking options:
https://www.mathnet.ru/eng/rcd122
https://www.mathnet.ru/eng/rcd/v18/i4/p453
This publication is cited in the following 6 articles:
Stefan Rauch-Wojciechowski, Maria Przybylska, “On Dynamics of Jellet's Egg. Asymptotic Solutions Revisited”, Regul. Chaotic Dyn., 25:1 (2020), 40–58
Tanriverdi V., “Dissipative Motion of a Spinning Heavy Symmetric TOP”, Eur. J. Phys., 41:5 (2020), 055001
Michael Vollmer, Klaus‐Peter Mölmann, “Stehaufkreisel – a never ending story”, Physik in unserer Zeit, 47:2 (2016), 96
Maria Przybylska, Stefan Rauch-Wojciechowski, “Dynamics of a Rolling and Sliding Disk in a Plane. Asymptotic Solutions, Stability and Numerical Simulations”, Regul. Chaotic Dyn., 21:2 (2016), 204–231
Maria Przybylska, Stefan Rauch-Wojciechowski, “Dynamics of a Rolling and Sliding Disk in a Plane. Asymptotic Solutions, Stability and Numerical Simulations”, –
I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Hamiltonization of elementary nonholonomic systems”, Russ. J. Math. Phys., 22:4 (2015), 444–453
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