[sleepyams]

I always wondered why that is for a long time (in basic physics that at least). It wasn't until grad school that I understood that position and velocity are enough to uniquely determine a trajectory on a manifold.

[dvt]

This is super interesting, is this generalizable to n-dimensional manifolds?

[sleepyams]

Yep! More specifically I'm basically talking about geodesics on Riemannian manifolds.