Abstract
The Chaplygin separation equation for a rolling axisymmetric ball has an algebraic expression for the effective potential V (z = cosθ, D, λ) 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 = cosθ. 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 \(\tfrac{{2\pi }} {T} \).
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