SmtC: Show me the Code
Ole Peter Smith
Instituto de Matemática e Estatística
Universidade Federal de Goiás
http://www.olesmith.com.br

Roulettes
Uma sociedade sera - sempre - avaliado
Pelo jeito que trata seus mais fracos.
Mahatma
< Epicycloid | Epitrochoid | Hypocycloid >

Epitrochoid: Extended Rolling of a Circle on the outside of a Circle

Formulas
$\underline{\mathbf{r}}(t)=r\left( \omega\underline{\mathbf{e}}(t) - \lambda\underline{\mathbf{e}}(\omega t) \right)$ $\underline{\mathbf{r}}'(t)=r\omega\left( \underline{\mathbf{f}}(t) - \lambda\underline{\mathbf{f}}(\omega t) \right)$
$\underline{\mathbf{r}}''(t)=r\omega\left( - \underline{\mathbf{e}}(t) + \lambda\omega\underline{\mathbf{e}}(\omega t) \right)$ $\widehat{\underline{\mathbf{r}}}'(t)=r\omega\left( - \underline{\mathbf{e}} + \lambda\underline{\mathbf{e}}(\omega t) \right)$
$v(t)^2=r^2\omega^2\left( 1+\lambda^2-2\lambda \cos{ (\omega-1)t} \right)$ $D(t)=r^2\omega^2\left( 1+\lambda^2 \omega - \lambda(\omega+1) \cos{ (\omega-1)t} \right)$
$\underline{\mathbf{t}}(t)=\frac{\underline{\mathbf{f}}(t)-\lambda\underline{\mathbf{f}}(\omega t)}{\sqrt{ 1+\lambda^2-2 \lambda \cos{(\omega-1)t} }}$ $\underline{\mathbf{n}}(t)=\frac{-\underline{\mathbf{e}}(t)+\lambda\underline{\mathbf{e}}(\omega t)}{\sqrt{ 1+\lambda^2-2 \lambda \cos{(\omega-1)t} }}$
$\psi(t)=\frac{ 1+\lambda^2 \omega - \lambda(\omega+1) \cos{ (\omega-1)t} }{1+\lambda^2-2\lambda \cos{ (\omega-1)t}}$ $\varphi(t)=\frac{ 1+\lambda^2-2\lambda \cos{ (\omega-1)t} }{1+\lambda^2 \omega - \lambda(\omega+1) \cos{ (\omega-1)t}}$
$\kappa(t)=\frac{1}{r \omega}\cdot \frac{ 1+\lambda^2 \omega - \lambda(\omega+1) \cos{ (\omega-1)t} }{\sqrt{1+\lambda^2-2\lambda \cos{ (\omega-1)t}}^3 }$ $\rho(t)=r \omega \cdot\frac{ \sqrt{1+\lambda^2-2\lambda \cos{ (\omega-1)t}}^3 }{1+\lambda^2 \omega - \lambda(\omega+1) \cos{ (\omega-1)t}}$
$\underline{\mathbf{c}}(t)=r\left( \omega(1-\varphi)\underline{\mathbf{e}}(t) - (1-\omega \varphi)\underline{\mathbf{e}}(\omega t) \right)$
$\underline{\mathbf{c}}'(t)=-$
$\mathcal{S}=\emptyset, |\lambda| \neq 1$
PDF: Epitrochoid
Parameters
Attr Name Default Current Values
RR $R$ 1.000000 1.0 1.0
Omega $\omega$ 2.000000 -
Lambda $\lambda$ 1.000000 -
Settings
Delay:
Type:
Every:
Use SVG Image tags:
Components
Curves
r:
r':
r'':
c:
c':
Functions
R:
Det:
\(\psi\):
\(\varphi\):
\(\kappa\):
\(\rho\):
Browse SVGs: Epitrochoid
Legends 4_Evolute 3_d2R 5_dEvolute 2_d1R 1_d0R
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=0.4
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=0.6
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=0.7
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=0.8
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=0.9
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=1.0
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=1.2
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=1.5
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=0.4
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=0.6
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=0.7
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=0.8
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=0.9
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=1.0
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=1.2
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=1.5
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=0.4
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=0.6
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=0.7
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=0.8
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=0.9
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=1.0
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=1.2
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=1.5
Legends 12_Phi 11_Psi 02_Det 14_Rho 01_v2 13_Kappa
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=0.4
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=0.6
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=0.7
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=0.8
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=0.9
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=1.0
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=1.2
Epitrochoid: Num R=1.0 \omega=2.0 \lambda=1.5
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=0.4
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=0.6
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=0.7
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=0.8
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=0.9
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=1.0
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=1.2
Epitrochoid: Num R=1.0 \omega=3.0 \lambda=1.5
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=0.4
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=0.6
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=0.7
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=0.8
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=0.9
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=1.0
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=1.2
Epitrochoid: Num R=1.0 \omega=4.0 \lambda=1.5
< Epicycloid | Epitrochoid | Hypocycloid >
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