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

O Homem é a espécie mais insana.
Venera um Deus invisível e destrói a Natureza visível…
Sem se aperceber de que esta Natureza, que ele destrói,
é o Deus invisível que ele venera

Hubert Reeves

< Other Curves | Cycloid | Trochoids >

Cycloid

Formulas

$\underline{\mathbf{r}}(t)=r\left( t\underline{\mathbf{i}} + \underline{\mathbf{j}} + \underline{\mathbf{q}}(t) \right)$	$\underline{\mathbf{r}}'(t)=r\left( \underline{\mathbf{i}} + \underline{\mathbf{p}}(t) \right)$
$\underline{\mathbf{r}}''(t)=-r\underline{\mathbf{q}}(t)$	$\widehat{\underline{\mathbf{r}}}'(t)=r\left( \underline{\mathbf{j}} + \underline{\mathbf{q}}(t) \right)$
$v(t)^2=2r^2\left( 1-\cos{t} \right)$	$D(t)=r^2\left( \cos{t}-1 \right)\leq 0$
$\frac{d}{dt} v(t)^2=2r^2\sin{t}$	$D'(t)=-r^2\sin{t}$
$\underline{\mathbf{t}}(t)=\frac{\underline{\mathbf{i}} + \underline{\mathbf{p}}(t)}{\sqrt{2(1-\cos{t})}}$	$\underline{\mathbf{n}}(t)=\frac{\underline{\mathbf{j}} + \underline{\mathbf{q}}(t)}{\sqrt{2(1-\cos{t})}}$
$\psi(t)=-\frac{1}{2}$	$\varphi(t)=-2$
$\kappa(t)=-\frac{1}{2\sqrt{2}r} \cdot \frac{1}{\sqrt{ 1-\cos{t}} }$	$\rho(t)=-2\sqrt{2}r \sqrt{ 1-\cos{t}}$
$\underline{\mathbf{c}}(t)=r\left( t\underline{\mathbf{i}} -\underline{\mathbf{j}} -\underline{\mathbf{q}}(t) \right)$
$\underline{\mathbf{c}}'(t)=r\left( \underline{\mathbf{i}} -\underline{\mathbf{p}}(t) \right)$
$\rho'(t)=-2\sqrt{2} r \frac{ \sin{t} }{ \sqrt{ 1-\cos{t}} }$
$\mathcal{S}=\left\{t \in \mathbb{R}~\left\|~~ 2 p \pi, ~p \in \mathbb{Z}\right.\right\}$
$\mathcal{E}=\left\{t \in \mathbb{R}~\left\|~~ (2 p+1) \pi, ~p \in \mathbb{Z}\right.\right\}$
$s(t)-s(t_0)=4\sqrt{2} r\left[ \cos{ \frac{t}{2} } \right]_{t}^{t_0} ,~t \in [0,2\pi[$