SmtC: Show me the Code!

SmtC: Show me the Code

Ole Peter Smith

Instituto de Matemática e Estatística

Universidade Federal de Goiás

http://www.olesmith.com.br

Roulettes

Quando eu dou de comer aos pobres
Me chamam de santo
Quando eu pergunto por que eles são pobres
Me chamam de comunista

Dom Helder Câmera

< Epitrochoid | Hypocycloid | Hypotrochoid >

Hypocycloid: Rolling a Circle on the inside of a Circle

Formulas

$\underline{\mathbf{r}}(t)=r\left( \omega\underline{\mathbf{e}}(t) - \underline{\mathbf{p}}(\omega t) \right)$	$\underline{\mathbf{r}}'(t)=r\omega\left( \underline{\mathbf{f}}(t) + \underline{\mathbf{q}}(\omega t) \right)$
$\underline{\mathbf{r}}''(t)=r\omega\left( - \underline{\mathbf{e}}(t) + \omega\underline{\mathbf{p}}(\omega t) \right)$	$\widehat{\underline{\mathbf{r}}}'(t)=r\omega\left( - \underline{\mathbf{e}}(t) - \underline{\mathbf{p}}(\omega t) \right)$
$v(t)^2=2r^2\omega^2\left( 1-\cos{ (\omega+1)t} \right)$	$D(t)=r^2\omega^2(1- \omega)\left( 1-\cos{(\omega+1)t} \right)$
$\frac{d}{dt} v(t)^2=2r^2\omega^2(\omega+1)\sin{ (\omega+1)t}$	$D'(t)=r^2\omega^2(1- \omega^2)\sin{(\omega+1)t}$
$\underline{\mathbf{t}}(t)=\frac{1}{\sqrt{2}}\cdot \frac{\underline{\mathbf{f}}(t)+\underline{\mathbf{q}}(\omega t)}{ \sqrt{1- \cos{ (\omega+1)t}} }$	$\underline{\mathbf{n}}(t)=-\frac{1}{\sqrt{2}}\cdot \frac{\underline{\mathbf{e}}(t)+\underline{\mathbf{p}}(\omega t)}{ \sqrt{1- \cos{ (\omega+1)t}} }$
$\psi(t)=\frac{1-\omega}{2}=\frac{2r-R}{2r}$	$\varphi(t)=\frac{2}{1-\omega}=\frac{2r}{2r-R}$
$\kappa(t)=\frac{1}{2\sqrt{2}}\cdot \frac{1-\omega}{ r\|\omega\|}\cdot \frac{1}{\sqrt{1-\cos{ (\omega+1)t}}}$	$\rho(t)=2\sqrt{2} \cdot \frac{ r \|\omega\|}{1-\omega} \cdot\sqrt{1-\cos{ (\omega+1)t}}$
$\underline{\mathbf{c}}(t)=\frac{R}{R-2r}\left( (R-r)\underline{\mathbf{e}}(t) - r\underline{\mathbf{p}}(\omega t+\pi) \right)$
$\underline{\mathbf{c}}'(t)=\frac{1+\omega}{1-\omega}\|\omega\|\left( \underline{\mathbf{e}}(t)+\underline{\mathbf{p}}(\omega t) \right)$
$\rho'(t)=\sqrt{2} r \|\omega\| \cdot \frac{ 1+\omega}{1-\omega} \cdot\frac{\sin{ (\omega+1)t}}{\sqrt{1-\cos{ (\omega+1)t}}}$