High frequency behaviour of a rolling ball and simplification of the Main Equation for the Tippe Top
(English)Manuscript (preprint) (Other academic)
The Chaplygin separation equation for a rolling axisymmetric ball has an algebraic expression for the effective potential V(z = cos θ, D, λ) which is difficult to analyse. We simplify this expression for the potential and find a 2-parameter family for when the potential becomes a rational function of z = cos θ. 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 ω3-dependence of the width of the nutational band, the depth of motion above V(zmin, D, λ) and the ω3-dependence of nutational frequency . These results have bearing for understanding the inverting motion of the Tippe Top, modeled by a rolling and gliding axisymmetric sphere.
Tippe top; rigid body; rolling sphere; integrals of motion; elliptic integrals.
IdentifiersURN: urn:nbn:se:liu:diva-88314OAI: oai:DiVA.org:liu-88314DiVA: diva2:602201