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High frequency behavior of a rolling ball and simplification of the separation equation
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2013 (English)In: Regulârnaâ i haoticeskaâ dinamika, ISSN 1560-3547, Vol. 18, no 3, 226-236 p.Article in journal (Refereed) Published
Abstract [en]

The Chaplygin separation equation for a rolling axisymmetric ball has an algebraic expression for the effective potential V (z = cos theta, D, lambda) that is difficult to analyze. We simplify this expression for the potential and find a 2-parameter family for when the potential becomes a rational function of z = cos theta. Then this separation equation becomes similar to the separation equation for the heavy symmetric top. For nutational solutions of a rolling sphere, we study a high frequency omega (3)-dependence of the width of the nutational band, the depth of motion above V(z (min),D, lambda) and the omega (3)-dependence of nutational frequency .

Place, publisher, year, edition, pages
MAIK Nauka/Interperiodica , 2013. Vol. 18, no 3, 226-236 p.
Keyword [en]
rigid body; rolling sphere; integrals of motion; elliptic integrals; tippe top
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-96144DOI: 10.1134/S1560354713030039ISI: 000319763900003OAI: diva2:640729
Available from: 2013-08-14 Created: 2013-08-14 Last updated: 2013-08-14

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Rutstam, Nils
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Mathematics and Applied MathematicsThe Institute of Technology
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