Simple EPs in 2D. definition of EP in 2D
Stability of 2D is tricky. Can use test points, but not always clear where they are pointing. Need lots of test points with very small \( \Delta_t \)
Is there a principle of Linear Stability Analysis in 2D? Yes, but we haven’t learned how to take the derivative (the linear approximation) of a 2D function. Will learn that next quarter.
Still true in 2D that all EPs are linear
How to make a 2D EP: mix and match 2 1D systems. Purely stable, purely unstable, saddle point.
Truly 2D EPs (not decomposable). Recall the example of the spring from ch 1. Derive dif eqs and EPs for stable spiral, unstable spiral, neutral center.
EPs in higher dimensions. Principle of mix and match still works. Case in 3D with a 2D unstable spiral and a 1D stable EP