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
Classifying Fixed Points of 2D Systems
► 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 Twitter: 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
► Next, classifying 2D fixed points of dynamical systems
Classifying Fixed Points of 2D Systems
► 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 Twitter: 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
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