From 363421f6d574f5a04ae295b9bb6fc95a00b0cced Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Wed, 2 Oct 2024 13:55:40 -0400 Subject: [PATCH] vault backup: 2024-10-02 13:55:40 --- .../2024-09-09 Frameworks and Review.md | 4 ++++ .../2024-09-16 Plane Diagrams.md | 4 +++- .../2024-09-23 More Phase Plane Stuff.md | 7 ++++++- .../How do we deal with nonlinearities?.png | Bin 0 -> 500492 bytes .../images/LINE Systems in the Plane.png | Bin 0 -> 353137 bytes .../images/Mode Diagram.png | Bin 0 -> 78973 bytes .../images/Nonlinear Planar Systems.png | Bin 0 -> 418013 bytes 7 files changed, 13 insertions(+), 2 deletions(-) create mode 100644 300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/How do we deal with nonlinearities?.png create mode 100644 300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/LINE Systems in the Plane.png create mode 100644 300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/Mode Diagram.png create mode 100644 300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/Nonlinear Planar Systems.png 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 0000000000000000000000000000000000000000..fe0ad7d9af9713549cb7b5135aeb0129c4c967c1 GIT binary patch literal 500492 zcmeFZg;yL~vp$RkmjQwWcY?dSCJ-#aHF$6f?ry=|Ap{LhfWcvKPeSlP1{++1+c%t? z^R9b;>%4!!x7Hncrkh?p-FsKxDx@v)?JW9HrTwA+gJq|gcvA1(m?-!~@dRUf$$>m=03z<=K| zLTPi6Xs8hWb(2GTCCD5thc73IB>Qh09oY`qe|@r|BuHJIHH+!rZ%so5c?JD1ZHkms zN5G4VHvJ*{@0|j`qbUfZ{A-I~C!_HaoHU-tFhu{CyT20rDfD0ZOQV(&7+UmMhgbdI z`ztF6N}TvFk_H5QMxrAl=>Ht`ucCyV#Ebig{omB^oSq6&#zd(6{J-2i!Rd?ZziHq} z2n9?qdC1j$`26o0jtqpU81cU~>i<;y|BChhRQx~2Ak+U@@&98v|9`ULg=9(8LNS3F z`)n~^uxM1P0i`FD%rMQKWexAy>NOyaEAHG 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