Reparametrization of a curve Given a parametrized curve, we know that its arc length parametrization is its unit speed reparametrization. However, I wanted to know if there was any generic procedure to find any other reparametrizations of the same curve, which are not unit speed, and are non trivial?

If you have one parametrization ${\bf X} = {\bf F}(t),\; a < t < b$, and $\varphi$ is any continuous monotonic function from another interval $(c,d)$ to  $(a,b)$, then another parametrization is ${\bf X} = {\bf F}(\varphi(s)),\; c < s < d$.  Every other parametrization is of this form. 
