Regular curve

Definition

A curve

$\gamma:\mathbb{R}\rightarrow\mathbb{R}^3$ usually (however

$\gamma:A\subseteq\mathbb{R}\rightarrow\mathbb{R}^n$ more generally) is called regular if all points (

$\in\text{Range}(\gamma)$ ) are regular

A point

$\gamma(t)$ is called regular of

$\dot\gamma\ne 0$ otherwise it is a Singular point

The curve

$\gamma(t)\mapsto(t,t^2)$ is regular however

$\gamma'(t)\mapsto(t^3,t^6)$ is not - it is not technically a reparametrisation

TODO: reparametrisation theorem