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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
High Frequency Behavior of a Rolling Ball and Simplification of the Separation Equation
Nils Rutstam Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden
Аннотация:
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 $\frac{2\pi}{T}$.
Ключевые слова:
rigid body, rolling sphere, integrals of motion, elliptic integrals, tippe top.
Поступила в редакцию: 13.04.2012 Принята в печать: 22.04.2013
Образец цитирования:
Nils Rutstam, “High Frequency Behavior of a Rolling Ball and Simplification of the Separation Equation”, Regul. Chaotic Dyn., 18:3 (2013), 226–236
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd111 https://www.mathnet.ru/rus/rcd/v18/i3/p226
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