From 9c94d1d60d1566ea3897e2f705f494741793e550 Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Mon, 9 Sep 2024 12:51:22 -0400 Subject: [PATCH] vault backup: 2024-09-09 12:51:22 --- .../2024-09-09 Frameworks and Review.md | 15 +++++++++++++++ 1 file changed, 15 insertions(+) diff --git a/300s School/301. ME 2016 - Nonlinear Dynamical Systems 1/2024-09-09 Frameworks and Review.md b/300s School/301. ME 2016 - Nonlinear Dynamical Systems 1/2024-09-09 Frameworks and Review.md index 640a12c5..4dd575fc 100644 --- a/300s School/301. ME 2016 - Nonlinear Dynamical Systems 1/2024-09-09 Frameworks and Review.md +++ b/300s School/301. ME 2016 - Nonlinear Dynamical Systems 1/2024-09-09 Frameworks and Review.md @@ -14,3 +14,18 @@ Well, a couple of places... 2. External fields 3. Material properties So we're stuck with them. But how do we deal with noninearities? + +## A nonlinear equation +$$ \dot{x} = \frac{dx}{dt} = 1-2\cos x$$ +How do you solve this? You can't use Laplace, you can't separate... +*insert very long expression that Bajaj wrote.* +Getting an analytical solution can be a PITA to obtain. For this reason: +**The general case is that nonlinear equations are unsolvable.** +This doesn't mean we can't learn things. We can describe these systems *qualitatively*. + +Really our options come down to: +- Solve exactly (Not likely to happen) +- Solve numerically +- Analyze qualitatively (~geometrically) +- Solve an approximation to the problem +We mix and match these approaches. \ No newline at end of file