MAE5790-8 Index theory and introduction to limit cycles
Index of a curve (with respect to a given vector field). Properties of the index. Index of a point. Using index theory to rule out closed trajectories. Some strange things: Index theory in biology. Hairy ball theorem. Combing a torus and connection to tokamaks and fusion. Index theory on compact orientable 2-manifolds. Limit cycles. Examples in science and engineering. Definitions, and why linear systems can't have limit cycles. Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 6.8, 7.0, 7.1.
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MAE5790-9 Testing for closed orbits
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Index Theory - Dynamical Systems | Lecture 20
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MAE5790-1 Course introduction and overview
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1. History of Algebraic Topology; Homotopy Equivalence - Pierre Albin
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We're 99.9% sure this pattern is true, but no one can prove it
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Divergence and curl: The language of Maxwell's equations, fluid flow, and more
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What Is a Limit Cycle? Introduction with Examples (Strogatz Ch. 7) | Part 1
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The Big Short (2015): The Jenga Scene – Explaining the Financial Collapse
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MAE5790-11 Averaging theory for weakly nonlinear oscillators
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How Maxwell's Equations Were Discovered
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The Hardest Questions in Physics | World Science Festival
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The French Do Not Care About Work
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MAE5790-20 Universal aspects of period doubling
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Defining Terms: Systems, Stability, and Limit Cycles
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Understanding Lagrange Multipliers Visually
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MAE5790-2 One dimensional Systems
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Introduction to Variational Calculus - Deriving the Euler-Lagrange Equation
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Limit Cycles - Dynamical Systems | Lecture 21
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Weird Things Happen When Energy Goes Negative
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