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300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-09 Frameworks and Review.md

@@ -123,3 +123,7 @@ Then the solution is
 $$\vec{x}(t) = e^{\bf{A}t}\vec{c} + e^{\bf{A}t} \int_{t_0}^t e^{-\bf{A}I} F(T) \delta T$$
 Then using the Laplace transform:
 $$e^{\bf{A}t} = \mathcal{L}^{-1} \{ (sI-\bf{A})^-1 \} $$
+# Written Notes
+
+![[How do we deal with nonlinearities?.png]]
+![[Mode Diagram.png]]

300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-16 Plane Diagrams.md

@@ -12,6 +12,8 @@ Recall that equilibrium points are fixed. P = Q = 0
 | Unstable      | Trajectories diverge from a point                                                                    |
 | Linear Center | An equilibrium point that has orbits around it                                                       |
 | Limit Cycle   | Happens a lot with nonlinear systems. Trajectories are pulled some target trajectory and stay there. |
-
+|               |                                                                                                      |
+# Written Notes
+![[LINE Systems in the Plane.png]]
 **Documentation**
 - [x] ME2016 Week 3 Class ⏳ 2024-09-16 ✅ 2024-09-16

300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-23 More Phase Plane Stuff.md

@@ -102,4 +102,9 @@ $$ {\bf J} =
 \left[ \matrix{ \frac{\partial P}{\partial x} &  \frac{\partial P}{\partial y} \\ \frac{\partial Q}{\partial x} & \frac{\partial Q}{\partial y}} \right] = 
 \left[ \matrix{ \beta -2\delta x - \gamma y & -\gamma x\\ - c y & b - 2dy - cx} \right]  
  $$
- Now we can actually do stuff with this in python instead of by hand.
+ Now we can actually do stuff with this in python instead of by hand.
+
+
+# Written Notes
+
+  ![[Nonlinear Planar Systems.png]]