Definition:Unit Tangent Vector of Curve Parameterized by Arc Length/3-Dimensional Real Vector Space
(Redirected from Definition:Unit Tangent Vector of Curve Parameterized by Arc Length in 3-Dimensional Real Vector Space)
Jump to navigation
Jump to search
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