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Phase Space of Rolling Solutions of the Tippe Top
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2007 (English)In: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, Vol. 3, 41-55 p.Article in journal (Refereed) Published
Abstract [en]

Equations of motion of an axially symmetric sphere rolling and sliding on a plane are usually taken as model of the tippe top. We study these equations in the nonsliding regime both in the vector notation and in the Euler angle variables when they admit three integrals of motion that are linear and quadratic in momenta. In the Euler angle variables (θ, ϕ, ψ) these integrals give separation equations that have the same structure as the equations of the Lagrange top. It makes it possible to describe the whole space of solutions by representing them in the space of parameters (D, λ, E) being constant values of the integrals of motion.

Place, publisher, year, edition, pages
2007. Vol. 3, 41-55 p.
Keyword [en]
Nonholonomic dynamics, Rigid body, Rolling sphere, Tippe top, Integrals of motivation
National Category
Mathematics Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-42016Local ID: 59560OAI: oai:DiVA.org:liu-42016DiVA: diva2:262871
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-07-21

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Glad, TorkelPetersson, DanielRauch-Wojciechowski, Stefan

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Glad, TorkelPetersson, DanielRauch-Wojciechowski, Stefan
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Automatic ControlThe Institute of TechnologyMathematics and Applied Mathematics
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MathematicsControl Engineering

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