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Completely Integrable Hamiltonian Systems | Poisson Bracket Series Expansions, Standard Map, Lect 14
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► Next: Lie series method for finding canonical transformations | infinite-dimensional Hamiltonian systems
► Previous: Casimir functions, Lie derivatives, Lie brackets, and compatible constants of motion
► Advanced Dynamics - Hamiltonian Systems and Nonlinear Dynamics
► Dr. Shane Ross, Virginia Tech professor (Caltech PhD)
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► See the entire playlist for the course:
Advanced Dynamics - Hamiltonian Systems and Nonlinear Dynamics
► Course lecture notes (PDF)
► Course lecture notes (OneNote)
► Continuation of this course on a related topic
Center manifolds, normal forms, and bifurcations
► A short, gentle introduction to Hamiltonian systems
Lecture 2020-04-07
Part of a graduate level course:
Advanced Dynamics (ESM/AOE 6314)
Spring Semester, 2020
► Courses and Playlists by Dr. Ross
📚Attitude Dynamics and Control
📚Nonlinear Dynamics and Chaos
📚Hamiltonian Dynamics
📚Three-Body Problem Orbital Mechanics
📚Lagrangian and 3D Rigid Body Dynamics
📚Center Manifolds, Normal Forms, and Bifurcations
Charles Conley index theory gradient system 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 Hamiltonian Hamilton streamlines weather vortex dynamics point vortices pendulum Newton's Second Law Conservation of Energy topology
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