Phase plane analysis (intro)
General · Mathematics
Study notes
Q: Classify the origin for x' = -y, y' = x. Sketch trajectories. A = [[0,-1],[1,0]]. Eigen: ±i (pure imaginary!). CENTER: closed circular orbits! Trajectories: x²+y² = const (circles!). Check: d/dt(x²+y²) = 2xx'+2yy' = -2xy+2yx = 0 ✓! (Harmonic oscillator - neutrally stable!)