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

PooPy Curves
O conhecimento adquirimos com os livros e os mestres.
A sabedoria aprendemos com o povo e os humildes.
Cora Coralina
< Parabola: PooPy Curves | Rolling on any Curve | Parabola, Rolling >
  • Fixed Curve: [; \underline{\textbf{R}}(t) ;]
  • Unit Normal: [; \underline{\textbf{N}}(t) ;]
  • Arc Length: [;s(t)=\int_{t_0}^t |\underline{\textbf{R}}'(t)|~dt;]
  • Rolling radius: [; r;]
  • Rolled Angle: [; \theta= \frac{s(t)}{r};]
  • Center of Rolling Circle: [; \underline{\textbf{R}}(t)+r \underline{\textbf{N}}(t) ;]
  • Rolling Vector: [; \pm r\underline{\underline{\textbf{D}}}(-\theta) \underline{\textbf{N}}(t) ;]
    [; \underline{\underline{\textbf{D}}}(\theta)= \left(\begin{array}{rr} \cos{\theta} & -\sin{\theta}\\ \sin{\theta} & \cos{\theta}\\ \end{array}\right);]
< Parabola: PooPy Curves | Rolling on any Curve | Parabola, Rolling >
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