Phase Portrait Introduction- Pendulum Example

In the geometric or graphical study of two-dimensional nonlinear ODEs, our goal is to determine all the qualitatively different system behaviors, that is, find the phase portrait. The pendulum example introduces the concept. ► Next, classifying 2D fixed points of dynamical systems https://youtu.be/7Ewe_tVa5Fs ► Nonlinear Dynamics and Chaos (online course). Playlist https://is.gd/NonlinearDynamics ► *Teacher Bio* Dr. Shane Ross, professor, Virginia Tech Background: Caltech PhD | worked at NASA/JPL & Boeing Research website http://shaneross.com ► More lectures posted regularly Be informed, subscribe https://is.gd/RossLabSubscribe​ ► *X* https://twitter.com/RossDynamicsLab ► *Make your own phase portrait* https://is.gd/phaseplane ► Course lecture notes (PDF) https://is.gd/NonlinearDynamicsNotes ► *Related Courses and Series Playlists by Dr. Ross* 📚Nonlinear Dynamics and Chaos https://is.gd/NonlinearDynamics 📚Lagrangian and 3D Rigid Body Dynamics https://is.gd/AnalyticalDynamics 📚Hamiltonian Dynamics https://is.gd/AdvancedDynamics 📚Center Manifolds, Normal Forms, and Bifurcations https://is.gd/CenterManifolds 📚3-Body Problem Orbital Dynamics Course https://is.gd/3BodyProblem 📚Space Manifolds https://is.gd/SpaceManifolds 📚Space Vehicle Dynamics https://is.gd/SpaceVehicleDynamics Reference: Steven Strogatz, "Nonlinear Dynamics and Chaos", Chapter 6: Phase Plane autonomous on the plane phase plane are introduced 2D ordinary differential equations 2d ODE vector field topology cylinder bifurcation robustness fragility cusp unfolding perturbations structural stability emergence critical point critical slowing down supercritical bifurcation subcritical bifurcations buckling beam model change of stability nonlinear dynamics dynamical systems differential equations dimensions phase space Poincare Strogatz graphical method Fixed Point Equilibrium Equilibria Stability Stable Point Unstable Point Linear Stability Analysis Vector Field Two-Dimensional 2-dimensional Functions #NonlinearDynamics #DynamicalSystems #DifferentialEquations #Bifurcation #SaddleNode #Bottleneck #Circle #CuspCatastrophe #CatastropheTheory #CuspBifurcation #CriticalPoint #buckling #PitchforkBifurcation #robust #StructuralStability #DifferentialEquations #dynamics #dimensions #PhaseSpace #PhasePortrait #PhasePlane #Poincare #Strogatz #GraphicalMethod #FixedPoints #EquilibriumPoints #Stability #StablePoint #UnstablePoint #Stability #LinearStability #LinearStabilityAnalysis #StabilityAnalysis #VectorField #TwoDimensional #Functions