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

Roulettes
Life is a mystery to be lived.
Not a problem to be solved.
Søren Kierkegaard.
< Cycloid | Trochoids | Epicycloid >

Trochoids

Formulas
$\underline{\mathbf{r}}(t)=r\left( t\underline{\mathbf{i}} + \underline{\mathbf{j}} + \lambda\underline{\mathbf{q}}(t) \right)$ $\underline{\mathbf{r}}'(t)=r\left( \underline{\mathbf{i}} + \lambda\underline{\mathbf{p}}(t) \right)$
$\underline{\mathbf{r}}''(t)=-r\lambda\underline{\mathbf{q}}(t)$ $\widehat{\underline{\mathbf{r}}}'(t)=r\left( \underline{\mathbf{j}} + \lambda\underline{\mathbf{q}}(t) \right)$
$v(t)^2=r^2\left( 1+\lambda^2-2\ \lambda \cos{t} \right)$ $D(t)=r^2\lambda\left( \cos{t}-\lambda \right)$
$\frac{d}{dt} v(t)^2=2r^2\lambda \sin{t}$ $D'(t)=-r^2\lambda\sin{t}$
$\underline{\mathbf{t}}(t)=\frac{\underline{\mathbf{i}} + \lambda\underline{\mathbf{p}}(t)}{\sqrt{ 1+\lambda^2-2 \lambda \cos{t} }}$ $\underline{\mathbf{n}}(t)=\frac{\underline{\mathbf{j}} + \lambda\underline{\mathbf{q}}(t)}{\sqrt{ 1+\lambda^2-2 \lambda \cos{t} }}$
$\psi(t)=\frac{\lambda\left( \cos{t}-\lambda \right)}{1+\lambda^2-2 \lambda \cos{t}}$ $\varphi(t)=\frac{1+\lambda^2-2 \lambda \cos{t}}{\lambda\left( \cos{t}-\lambda \right)}$
$\kappa(t)=\frac{1}{r} \cdot \frac{ \lambda\left(\cos{t}-\lambda\right)}{(1+\lambda^2-2 \lambda \cos{t})^{3/2}}$ $\rho(t)=r \cdot \frac{ (1+\lambda^2-2 \lambda \cos{t})^{3/2}}{\lambda\left(\cos{t}-\lambda\right)}$
$\underline{\mathbf{c}}(t)=r\left( t\underline{\mathbf{i}} +\left[ 1+\varphi(t) \right]\underline{\mathbf{j}} +\lambda\left[ 1+\varphi(t) \right]\underline{\mathbf{q}}(t) \right)$
$\underline{\mathbf{c}}'(t)=r\left( \underline{\mathbf{i}} +\varphi'(t)\underline{\mathbf{j}} +\lambda \varphi'(t)\underline{\mathbf{q}}(t)+\lambda\left[ 1+\varphi(t) \right]\underline{\mathbf{p}}(t) \right)$
$\rho'(t)=-r\lambda\frac{\sqrt{r^2\left( 1+\lambda^2-2\ \lambda \cos{t} \right)}}{\lambda^2(\cos{t}+\lambda)^2}\cdot\sin{t}\cdot\left( 1-2\lambda^2+\lambda \cos{t} \right)$
$\mathcal{S}=\left\{t \in \mathbb{R}~\left|~~ 2 p \pi, ~p \in \mathbb{Z}\right.\right\}$
$\mathcal{E}=\left\{t \in \mathbb{R}~\left|~~ (2 p+1) \pi, ~p \in \mathbb{Z}\right.\right\}$
$s(t)-s(t_0)=r\int_{t_0}^t \sqrt{1+\lambda^2-2\lambda \cos{t}}~dt$
PDF: Trochoid
Parameters
Attr Name Default Current Values
r $r$ 1.000000 1.0 1.0
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: Trochoid
Legends 4_Evolute 3_d2R 5_dEvolute 2_d1R 1_d0R
Trochoid: Num r=1.0 \lambda=0.1
Trochoid: Num r=1.0 \lambda=0.2
Trochoid: Num r=1.0 \lambda=0.3
Trochoid: Num r=1.0 \lambda=0.4
Trochoid: Num r=1.0 \lambda=0.5
Trochoid: Num r=1.0 \lambda=0.6
Trochoid: Num r=1.0 \lambda=0.7
Trochoid: Num r=1.0 \lambda=0.8
Trochoid: Num r=1.0 \lambda=0.9
Trochoid: Num r=1.0 \lambda=1.0
Trochoid: Num r=1.0 \lambda=1.1
Trochoid: Num r=1.0 \lambda=1.2
Trochoid: Num r=1.0 \lambda=1.3
Trochoid: Num r=1.0 \lambda=1.4
Trochoid: Num r=1.0 \lambda=1.5
Trochoid: Num r=1.0 \lambda=1.6
Trochoid: Num r=1.0 \lambda=1.7
Trochoid: Num r=1.0 \lambda=1.8
Trochoid: Num r=1.0 \lambda=1.9
Trochoid: Num r=1.0 \lambda=2.0
Legends 12_Phi 11_Psi 02_Det 14_Rho 01_v2 13_Kappa
Trochoid: Num r=1.0 \lambda=0.1
Trochoid: Num r=1.0 \lambda=0.2
Trochoid: Num r=1.0 \lambda=0.3
Trochoid: Num r=1.0 \lambda=0.4
Trochoid: Num r=1.0 \lambda=0.5
Trochoid: Num r=1.0 \lambda=0.6
Trochoid: Num r=1.0 \lambda=0.7
Trochoid: Num r=1.0 \lambda=0.8
Trochoid: Num r=1.0 \lambda=0.9
Trochoid: Num r=1.0 \lambda=1.0
Trochoid: Num r=1.0 \lambda=1.1
Trochoid: Num r=1.0 \lambda=1.2
Trochoid: Num r=1.0 \lambda=1.3
Trochoid: Num r=1.0 \lambda=1.4
Trochoid: Num r=1.0 \lambda=1.5
Trochoid: Num r=1.0 \lambda=1.6
Trochoid: Num r=1.0 \lambda=1.7
Trochoid: Num r=1.0 \lambda=1.8
Trochoid: Num r=1.0 \lambda=1.9
Trochoid: Num r=1.0 \lambda=2.0
< Cycloid | Trochoids | Epicycloid >
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