From 47eedad1667146deaf776780c88b6a6c48e6297e Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Mon, 28 Oct 2024 14:49:03 -0400 Subject: [PATCH] vault backup: 2024-10-28 14:49:03 --- .../2024-10-28 Stability.md | 15 +++++++++++++++ .../Untitled.md | 0 2 files changed, 15 insertions(+) create mode 100644 300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-10-28 Stability.md delete mode 100644 300s School/ME 2016 - Nonlinear Dynamical Systems 1/Untitled.md diff --git a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-10-28 Stability.md b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-10-28 Stability.md new file mode 100644 index 000000000..eed8814c7 --- /dev/null +++ b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-10-28 Stability.md @@ -0,0 +1,15 @@ +We're talking all about stability + +>[!note] Autonomous vs. Nonautonomous Systems +>**Autonomous**: $\dot x = X(x)$ +>**Non-Autonomous:** $\dot x = X(x,t)$ + +We talk about stability usually meaning that things settle to an equilibrium point. But this isn't the only way to look at things... + +# Poincare Stability (Path Stability) +For autonomous systems. Basically, adhere to a path for distrubances. +## Types of Paths +### Standard Path +$x^*$ is a phase path or equilibrium point whose stability is in question. +This is a solution of $\dot x = X$ +### 'Half-path' or 'Half-orbit' or 'Semi-orbit' diff --git a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/Untitled.md b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/Untitled.md deleted file mode 100644 index e69de29bb..000000000