Definition:Regular Curve/3-Dimensional Real Vector Space
< Definition:Regular Curve(Redirected from Definition:Regular Curve in 3-Dimensional Real Vector Space)
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Definition
Let $\alpha : I \to \R^3$ be a smooth curve.
$\alpha$ is said to be regular if and only if:
- $\forall t \in I : \map {\alpha'} t \ne \bszero_{\R^3}$
where:
- $\alpha'$ denotes the derivative of $\alpha$
- $\bszero_{\R^3}$ denotes the zero vector in $\R^3$
Also see
- Definition:Regular Curve: A more general definition for smooth manifolds
Sources
- 2016: Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces (2nd ed.): $1$-$3$: Regular Curves; Arc Length