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I'm looking to write up a paper involving parametric curves, and I am in search of a notation that, at a glance, distinguishes curve vectors whose parameter is nothing unusual, i.e.

$$\mathbf{r}(t)=\begin{bmatrix} x(t) \\ y(t) \end{bmatrix} , \text{where }\left|\frac{\mathrm{d}\mathbf{r}(t)}{\mathrm{d}t}\right| \ne 1$$

versus those whose parameter is equal to the arc-length of the curve: a curve with arc-length parameterisation, i.e.

$$\mathbf{r}(s)=\begin{bmatrix} x(s) \\ y(s) \end{bmatrix} , \text{where }\left|\frac{\mathrm{d}\mathbf{r}(s)}{\mathrm{d}s}\right| = 1$$

Has anyone come across in their travels a notation that distinguishes type $\mathbf{r}(t)$ from type $\mathbf{r}(s)$ other than the choice of parameter variable ($t$ v.s. $s$)? Using specific parameter variables isn't much of an option since I will need to use different variables and, in cases, use the same parameter variable in both types of these curves.

Second best thing, if you have a suggestion for the notation, that would also be appreciated!

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It is just a convention. But the choice must be stated if there would be ambiguity:

I use primes to denote differentiation with respect to arc length e.g., $$r', r'', \frac{r r''}{1+r^{'2}} = (r-r')$$

and dots to denote differentiation with respect to a parameter $t,$ e.g., $$d \dot r, \ddot r, \frac{r \ddot r}{1+\dot r^2} = (r-\dot r)$$

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