From 2fc7a0951824f845f9ce916e91d28370365d5170 Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Mon, 23 Sep 2024 13:43:04 -0400 Subject: [PATCH] vault backup: 2024-09-23 13:43:04 --- .../2024-09-23 Temporary Title.md | 9 ++++++++- .../images/Pasted image 20240923133628.png | Bin 0 -> 291021 bytes .../images/Pasted image 20240923133900.png | Bin 0 -> 374291 bytes 3 files changed, 8 insertions(+), 1 deletion(-) create mode 100644 300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/Pasted image 20240923133628.png create mode 100644 300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/Pasted image 20240923133900.png diff --git a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-23 Temporary Title.md b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-23 Temporary Title.md index aba4dbfd..6abae506 100644 --- a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-23 Temporary Title.md +++ b/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? \ No newline at end of file +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! \ No newline at end of file diff --git a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/Pasted image 20240923133628.png b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/images/Pasted image 20240923133628.png new file mode 100644 index 0000000000000000000000000000000000000000..b684693e7fca6b443969d761c41af1e6eb71f656 GIT binary patch literal 291021 zcmeFZRahKR(=M729D=*M1t+)@+}+)6a0Z7EAUFiqf#4F{$>171K+wSnmYG2VgkWd# z{d@28?fY|i`lfs4>0aGkRjXFj`&MQI^+z@dBCt#fw+i=%|Q) z07t#Kh#j)8oQgg=VhcsLk3;+>_fs(T)AMxn3$XEVc;V#X32@-@wexXs@bGo^^gDai zFNHXX>)%Q5d>m~2Ts%GK^j!cBFEkJb`~q}(4qkNpy!>zJc=^Nxgv1aB+8T5U^7`X? zp}goU~2*_ost5F@E5D-*If#%;D{+D_Zpi${~XBY%H7l9j`oSeCV5*`Hc(dl> zj*L{<-@grm!E$3_P+I%?JZ^4o)RmNCT>t<<#Dlqec;q9r+_F~pPj(tsR>g?Bb$>s~ 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