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2013
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# Nils Rutstam

 Rauch-Wojciechowski S., Rutstam N. Dynamics of the Tippe Top — Properties of Numerical Solutions Versus the Dynamical Equations 2013, vol. 18, no. 4, pp.  453-467 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. Keywords: Tippe Top, rigid body, nonholonomic mechanics, numerical solutions Citation: Rauch-Wojciechowski S., Rutstam N.,  Dynamics of the Tippe Top — Properties of Numerical Solutions Versus the Dynamical Equations, Regular and Chaotic Dynamics, 2013, vol. 18, no. 4, pp. 453-467 DOI:10.1134/S1560354713040084
 Rutstam N. High Frequency Behavior of a Rolling Ball and Simplification of the Separation Equation 2013, vol. 18, no. 3, pp.  226-236 Abstract 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 $\frac{2\pi}{T}$. Keywords: rigid body, rolling sphere, integrals of motion, elliptic integrals, tippe top Citation: Rutstam N.,  High Frequency Behavior of a Rolling Ball and Simplification of the Separation Equation, Regular and Chaotic Dynamics, 2013, vol. 18, no. 3, pp. 226-236 DOI:10.1134/S1560354713030039