vault backup: 2024-09-23 13:43:04

300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-23 Temporary Title.md

@@ -69,4 +69,11 @@ For $\bf J$:
 Then:
 - $\theta$ is 0, $\Delta = \omega^2 >0$, center, marginally stable
 - $\theta = n \pi$, $\Delta = - \omega^2 <0$, saddle. Unstable
-What does the phase plane look like?
+What does the phase plane look like?
+![[Pasted image 20240923133628.png]]
+How do we know which way the saddle points will kick us? The eigenvalues. The centers correlate to when the pendulum can't go around and around, the saddles are when you're wildin.
+
+### Damped
+What about when we have damping?
+![[Pasted image 20240923133900.png]]
+Now we have stable spirals!