I've read a few papers in dynamical systems where the model equations are sets of ODEs, with the state space, say, the spatial variables x, y, z, and an angle variable phi all evolving forward in time. The simulations match the 3D lab experiments very well too.
Why does this happen?
I would think that 3D phenomenon needs to be modeled with PDEs, using partial derivatives to describe, say, a change in x per change in y.
How do ODEs make good model equations?