I'm reading Vladimir Arnold's differential mechanics textbook and came across this definition and figure:
Despite his drawing I still found it vague and hard to understand precisely what he means. Right now I imagine this: The tangent vectors at every point of $y = x^2$ being rotated and translated to make the tangency of $\dot y = 2x$ . However, I would like to see this drawn on in perhaps some simple diagram, and should I be incorrect then a correct drawing on some simple monomial like $x^2$. I am trying to understand exterior and differential forms better, so I feel it is crucial I can visualize this without hallucinating an incorrect intuition.