From f4fc6160dccb15fb84b95aa092c508cc50fe5760 Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Mon, 23 Sep 2024 14:38:31 -0400 Subject: [PATCH] vault backup: 2024-09-23 14:38:31 --- .../2024-09-23 Temporary Title.md | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) 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 a94ed9fb..5adaa570 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 @@ -97,4 +97,9 @@ $$\dot y = y(b - d y - c x) = by - dy^2 -cxy$$ >[!note] Coupling Terms >$\gamma x y$ and $c x y$ are coupling terms. >These equations are coupled because of these. Without them x and y would just be doing their own thing. - +## Computing our Jacobian +$$ {\bf J} = +\left[ \matrix{ \frac{\partial P}{\partial x} & \frac{\partial P}{\partial y} \\ \frac{\partial Q}{\partial x} & \frac{\partial Q}{\partial y}} \right] = +\left[ \matrix{ \beta -2\delta x - \gamma y & -\gamma x\\ - c y & b - 2dy - cx} \right] + $$ + Now we can actually do stuff with this in SymPy \ No newline at end of file