The position vector, as a function of time and in Cartesian coordinates, of a particle is the following:
$$\vec{r}(t) = (5t^2-6t)\vec{e}_1 + \cos(\sin(t))\vec{e}_2+ (8t-5)\vec{e}_3$$
I have that vector expressed in Cartesian coordinates, how it would be expressed in cylindrical coordinates. I've read many manuals and seen videos, but I can't understand it. If you want to do it with this vector instead, you can do it with another one.
I know it seems like a more appropriate question for the Physics forum, but from there I have been referred here.