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Tippe Top Toy

Notebook is attached. A Tippe Top is a kind of top.

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When a tippe top is spun at a high angular velocity, its handle slowly tilts downwards more and more until it lifts the body of the top off the ground with the stem pointing downward. As the top's spinning rate slows, it loses stability and eventually topples over.

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POSTED BY: Mariusz Iwaniuk

This is great. I enjoy the fact the quite complex math equations are neatly pinpoint the effect. Math is great. If in your notebook I take equations from NDSolveValue and denote them by, say, eq, then this

eq // Column // TeXForm 

will give me the nice MathML below. So Community is great too for simple parsing of LaTeX type of math right from Mathematica. Adding here you reference:

Analysis of Dynamics of the Tippe Top Nils Rutstam. Linköping Studies in Science and Technology.Dissertations, No .1500, Department of Mathematics Linköping University, SE --- 581 83, Linköping, Sweden Linköping 2013.

$$ \begin{array}{l} \theta ''(t)=\frac{\sin (\theta (t)) \left(-\alpha R gn+i1 \cos (\theta (t)) \phi '(t)^2-i3 \omega 3(t) \phi '(t)\right)}{i1}+\frac{\mu R gn Vx(t) (1-\alpha \cos (\theta (t)))}{i1} \ \phi ''(t)=\frac{\csc (\theta (t)) \left(\mu (-R) gn Vy(t) (\alpha -\cos (\theta (t)))+i3 \omega 3(t) \theta '(t)-2 i_1 \theta '(t) \cos (\theta (t)) \phi '(t)\right)}{i_1} \ \omega 3'(t)=-\frac{\mu R gn \sin (\theta (t)) Vy(t)}{i3} \ Vx'(t)=-\frac{\mu gn Vx(t) \left(m R^2 (1-\alpha \cos (\theta (t)))^2+i1\right)}{i_1 m}+\frac{R \sin (\theta (t)) \left(\alpha R gn (1-\alpha \cos (\theta (t)))-i1 \alpha \left(\theta '(t)^2+\sin ^2(\theta (t)) \phi '(t)^2\right)+\omega 3(t) \phi '(t) \left(i3 (1-\alpha \cos (\theta (t)))-i1\right)\right)}{i1}+V_y(t) \phi '(t) \ Vy'(t)=-\frac{\mu gn Vy(t) \left(i3 m R^2 (\alpha -\cos (\theta (t)))^2+i1 m R^2 \sin ^2(\theta (t))+i1 i3\right)}{i1 i_3 m}+\frac{R \omega 3(t) \theta '(t) \left(i3 (\alpha -\cos (\theta (t)))+i1 \cos (\theta (t))\right)}{i1}-V_x(t) \phi '(t) \ \psi '(t)=\omega _3(t) \ \theta (0)=0.1 \ \theta '(0)=0 \ \phi (0)=0 \ \phi '(0)=0 \ \omega _3(0)=160 \ V_x(0)=0 \ V_y(0)=0 \ \psi (0)=0 \ \end{array} $$

POSTED BY: Sam Carrettie
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