diff --git a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-09 Frameworks and Review.md b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-09 Frameworks and Review.md index 6e319fb4e..0b85dd5a4 100644 --- a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-09 Frameworks and Review.md +++ b/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]] \ No newline at end of file diff --git a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-16 Plane Diagrams.md b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-16 Plane Diagrams.md index 4f645443a..91030a010 100644 --- a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-16 Plane Diagrams.md +++ b/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 \ No newline at end of file diff --git a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-23 More Phase Plane Stuff.md b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-23 More Phase Plane Stuff.md index e0f67711d..3ac2a637a 100644 --- a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-23 More Phase Plane Stuff.md +++ b/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. \ No newline at end of file + Now we can actually do stuff with this in python instead of by hand. + + +# Written Notes + + ![[Nonlinear Planar Systems.png]] \ No newline at end of file diff --git a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/How do we deal with nonlinearities?.png b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/How do we deal with nonlinearities?.png new file mode 100644 index 000000000..fe0ad7d9a Binary files /dev/null and b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/How do we deal with nonlinearities?.png differ diff --git a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/LINE Systems in the Plane.png b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/LINE Systems in the Plane.png new file mode 100644 index 000000000..b72c4edac Binary files /dev/null and b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/LINE Systems in the Plane.png differ diff --git a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/Mode Diagram.png b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/Mode Diagram.png new file mode 100644 index 000000000..854ebbd21 Binary files /dev/null and b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/Mode Diagram.png differ diff --git a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/Nonlinear Planar Systems.png b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/Nonlinear Planar Systems.png new file mode 100644 index 000000000..44848cfb0 Binary files /dev/null and b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/Nonlinear Planar Systems.png differ