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

Roulettes
A seriedade dos acontecimentos da minha época.
Me enche de esperança.
Karl Marx
< Hypocycloid | Hypotrochoid | Taxist Model >

Hypotrochoid: Extended Rolling of a Circle on the inside of a Circle

Formulas
$\underline{\mathbf{r}}(t)=r\left\{ \omega\underline{\mathbf{e}}(t) - \lambda\underline{\mathbf{p}}(\omega t) \right\}$ $\underline{\mathbf{r}}'(t)=r\omega\left\{ \underline{\mathbf{f}}(t) + \lambda\underline{\mathbf{q}}(\omega t) \right\}$
$\underline{\mathbf{r}}''(t)=r\omega\left\{ - \underline{\mathbf{e}}(t) + \lambda\omega\underline{\mathbf{p}}(\omega t) \right\}$ $\widehat{\underline{\mathbf{r}}}'(t)=r\omega\left\{ - \underline{\mathbf{e}}(t) - \lambda\underline{\mathbf{p}}(\omega t) \right\}$
$v(t)^2=r^2\omega^2\left\{ 1+\lambda^2-2\lambda \cos{ (\omega+1)t} \right\}$ $D(t)=r^2\omega^2\left\{ 1-\lambda^2 \omega + \lambda(\omega-1) \cos{ (\omega+1)t} \right\}$
$\underline{\mathbf{t}}(t)=\frac{r\omega\left\{ \underline{\mathbf{f}}(t) + \lambda\underline{\mathbf{q}}(\omega t) \right\}}{\sqrt{r^2\omega^2\left\{ 1+\lambda^2-2\lambda \cos{ (\omega+1)t} \right\}}} \cdot $ $\underline{\mathbf{n}}(t)=\frac{r\omega\left\{ - \underline{\mathbf{e}}(t) - \lambda\underline{\mathbf{p}}(\omega t) \right\}}{\sqrt{r^2\omega^2\left\{ 1+\lambda^2-2\lambda \cos{ (\omega+1)t} \right\}}} \cdot $
$\psi(t)=\frac{1}{\varphi(t)}$ $\varphi(t)=\frac{ 1+\lambda^2-2\lambda \cos{ (\omega+1)t} }{1-\lambda^2 \omega + \lambda(\omega-1) \cos{ (\omega+1)t}}$
$\kappa(t)=\frac{1}{ r \omega }\cdot \frac{ 1-\lambda^2 \omega + \lambda(\omega-1) \cos{ (\omega+1)t} }{ \sqrt{1+\lambda^2-2\lambda \cos{ (\omega+1)t}}^3 }$ $\rho(t)=\frac{(r^2\omega^2\left\{ 1+\lambda^2-2\lambda \cos{ (\omega+1)t} \right\})^{3/2}}{ (r^2\omega^2\left\{ 1-\lambda^2 \omega + \lambda(\omega-1) \cos{ (\omega+1)t} \right\}}$
$\underline{\mathbf{c}}(t)=r\left\{ \omega(1-\varphi(t))\underline{\mathbf{e}}(t) - \lambda (1+\omega \varphi(t))\underline{\mathbf{p}}(\omega t) \right\}$
$\underline{\mathbf{c}}'(t)=-$
PDF: Hypotrochoid
Parameters
Attr Name Default Current Values
RR $R$ 3.000000 1.0 1.0
r $r$ 1.000000 -
b $b$ -2.000000 -
Settings
Delay:
Type:
Every:
Use SVG Image tags:
Components
Curves
r:
r':
r'':
c:
c':
Functions
R:
Det:
\(\psi\):
\(\varphi\):
\(\kappa\):
\(\rho\):
Browse SVGs: Hypotrochoid
Legends 4_Evolute 3_d2R 5_dEvolute 2_d1R 1_d0R
Hypotrochoid: Num R=1.0 r=0.2 b=0.0
Hypotrochoid: Num R=1.0 r=0.2 b=1.0
Hypotrochoid: Num R=1.0 r=0.2 b=2.0
Hypotrochoid: Num R=1.0 r=0.2 b=3.0
Hypotrochoid: Num R=1.0 r=0.2 b=4.0
Hypotrochoid: Num R=1.0 r=0.2 b=5.0
Hypotrochoid: Num R=1.0 r=0.25 b=0.0
Hypotrochoid: Num R=1.0 r=0.25 b=1.0
Hypotrochoid: Num R=1.0 r=0.25 b=2.0
Hypotrochoid: Num R=1.0 r=0.25 b=3.0
Hypotrochoid: Num R=1.0 r=0.25 b=4.0
Hypotrochoid: Num R=1.0 r=0.25 b=5.0
Hypotrochoid: Num R=1.0 r=0.333333333333 b=0.0
Hypotrochoid: Num R=1.0 r=0.333333333333 b=1.0
Hypotrochoid: Num R=1.0 r=0.333333333333 b=2.0
Hypotrochoid: Num R=1.0 r=0.333333333333 b=3.0
Hypotrochoid: Num R=1.0 r=0.333333333333 b=4.0
Hypotrochoid: Num R=1.0 r=0.333333333333 b=5.0
Hypotrochoid: Num R=1.0 r=0.5 b=0.0
Hypotrochoid: Num R=1.0 r=0.5 b=1.0
Hypotrochoid: Num R=1.0 r=0.5 b=2.0
Hypotrochoid: Num R=1.0 r=0.5 b=3.0
Hypotrochoid: Num R=1.0 r=0.5 b=4.0
Hypotrochoid: Num R=1.0 r=0.5 b=5.0
Hypotrochoid: Num R=1.0 r=2.0 b=0.0
Hypotrochoid: Num R=1.0 r=2.0 b=1.0
Hypotrochoid: Num R=1.0 r=2.0 b=2.0
Hypotrochoid: Num R=1.0 r=2.0 b=3.0
Hypotrochoid: Num R=1.0 r=2.0 b=4.0
Hypotrochoid: Num R=1.0 r=2.0 b=5.0
Hypotrochoid: Num R=1.0 r=3.0 b=0.0
Hypotrochoid: Num R=1.0 r=3.0 b=1.0
Hypotrochoid: Num R=1.0 r=3.0 b=2.0
Hypotrochoid: Num R=1.0 r=3.0 b=3.0
Hypotrochoid: Num R=1.0 r=3.0 b=4.0
Hypotrochoid: Num R=1.0 r=3.0 b=5.0
Hypotrochoid: Num R=1.0 r=4.0 b=0.0
Hypotrochoid: Num R=1.0 r=4.0 b=1.0
Hypotrochoid: Num R=1.0 r=4.0 b=2.0
Hypotrochoid: Num R=1.0 r=4.0 b=3.0
Hypotrochoid: Num R=1.0 r=4.0 b=4.0
Hypotrochoid: Num R=1.0 r=4.0 b=5.0
Hypotrochoid: Num R=1.0 r=5.0 b=0.0
Hypotrochoid: Num R=1.0 r=5.0 b=1.0
Hypotrochoid: Num R=1.0 r=5.0 b=2.0
Hypotrochoid: Num R=1.0 r=5.0 b=3.0
Hypotrochoid: Num R=1.0 r=5.0 b=4.0
Hypotrochoid: Num R=1.0 r=5.0 b=5.0
Legends 12_Phi 11_Psi 02_Det 14_Rho 01_v2 13_Kappa
Hypotrochoid: Num R=1.0 r=0.2 b=0.0
Hypotrochoid: Num R=1.0 r=0.2 b=1.0
Hypotrochoid: Num R=1.0 r=0.2 b=2.0
Hypotrochoid: Num R=1.0 r=0.2 b=3.0
Hypotrochoid: Num R=1.0 r=0.2 b=4.0
Hypotrochoid: Num R=1.0 r=0.2 b=5.0
Hypotrochoid: Num R=1.0 r=0.25 b=0.0
Hypotrochoid: Num R=1.0 r=0.25 b=1.0
Hypotrochoid: Num R=1.0 r=0.25 b=2.0
Hypotrochoid: Num R=1.0 r=0.25 b=3.0
Hypotrochoid: Num R=1.0 r=0.25 b=4.0
Hypotrochoid: Num R=1.0 r=0.25 b=5.0
Hypotrochoid: Num R=1.0 r=0.333333333333 b=0.0
Hypotrochoid: Num R=1.0 r=0.333333333333 b=1.0
Hypotrochoid: Num R=1.0 r=0.333333333333 b=2.0
Hypotrochoid: Num R=1.0 r=0.333333333333 b=3.0
Hypotrochoid: Num R=1.0 r=0.333333333333 b=4.0
Hypotrochoid: Num R=1.0 r=0.333333333333 b=5.0
Hypotrochoid: Num R=1.0 r=0.5 b=0.0
Hypotrochoid: Num R=1.0 r=0.5 b=1.0
Hypotrochoid: Num R=1.0 r=0.5 b=2.0
Hypotrochoid: Num R=1.0 r=0.5 b=3.0
Hypotrochoid: Num R=1.0 r=0.5 b=4.0
Hypotrochoid: Num R=1.0 r=0.5 b=5.0
Hypotrochoid: Num R=1.0 r=2.0 b=0.0
Hypotrochoid: Num R=1.0 r=2.0 b=1.0
Hypotrochoid: Num R=1.0 r=2.0 b=2.0
Hypotrochoid: Num R=1.0 r=2.0 b=3.0
Hypotrochoid: Num R=1.0 r=2.0 b=4.0
Hypotrochoid: Num R=1.0 r=2.0 b=5.0
Hypotrochoid: Num R=1.0 r=3.0 b=0.0
Hypotrochoid: Num R=1.0 r=3.0 b=1.0
Hypotrochoid: Num R=1.0 r=3.0 b=2.0
Hypotrochoid: Num R=1.0 r=3.0 b=3.0
Hypotrochoid: Num R=1.0 r=3.0 b=4.0
Hypotrochoid: Num R=1.0 r=3.0 b=5.0
Hypotrochoid: Num R=1.0 r=4.0 b=0.0
Hypotrochoid: Num R=1.0 r=4.0 b=1.0
Hypotrochoid: Num R=1.0 r=4.0 b=2.0
Hypotrochoid: Num R=1.0 r=4.0 b=3.0
Hypotrochoid: Num R=1.0 r=4.0 b=4.0
Hypotrochoid: Num R=1.0 r=4.0 b=5.0
Hypotrochoid: Num R=1.0 r=5.0 b=0.0
Hypotrochoid: Num R=1.0 r=5.0 b=1.0
Hypotrochoid: Num R=1.0 r=5.0 b=2.0
Hypotrochoid: Num R=1.0 r=5.0 b=3.0
Hypotrochoid: Num R=1.0 r=5.0 b=4.0
Hypotrochoid: Num R=1.0 r=5.0 b=5.0
< Hypocycloid | Hypotrochoid | Taxist Model >
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