Definition:Unit Tangent Vector of Curve Parameterized by Arc Length/3-Dimensional Real Vector Space

Definition

Let $\alpha : I \to \R^3$ be a (smooth) curve parameterized by arc length.

The unit tangent vector of $\alpha$ at $s$ is defined as:

$\map t s := \map {\alpha '} s$

where:

$\alpha '$ denotes the derivative of $\alpha$

Sources

• 2016: Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces (2nd ed.): $1$-$5$: The Local Theory of Curves Parametrized by Arc Length