Poincar Map of Parametrically Forced Pendulum EuiSun Lee

Poincaré Map of Parametrically Forced Pendulum Eui-Sun Lee Department of Physics Kangwon National University

Solving The Second-Order Differential Equation • A second-order differential equation is reduced to two

Discrete time system • Poincaré Map Parametrically forced pendulum The Poincaré Map(Solid circle) is

Symmetry The Poincaré Map has an Inversion Symmetry such that In The PFP, The

Summary 1. A dynamical system is described by differential equation mathematically. 2. The Poincaré

Slides: 5

Poincaré Map of Parametrically Forced Pendulum Eui-Sun Lee Department of Physics Kangwon National University • Continuous time system • Parametrically forced pendulum(PFP) : the angular position the damping coefficient the amplitude of the external driving force of period one the undamped natural frequency of the unforced pendulum • These equation have the Inversion symmetry

Solving The Second-Order Differential Equation • A second-order differential equation is reduced to two first-order differential equation. • Forth-order Runge-Kutta method Initial value: for( i=0, 1, 2…, N) Step width a number of steps

Discrete time system • Poincaré Map Parametrically forced pendulum The Poincaré Map(Solid circle) is The Stroboscopic sampling of Flow(Solid Line). • The Poincaré Map(T) is Convenient for Finding The Periodic Orbit, Analyzing the Stability of The Orbit, Showing up Fractal Geometric Properties of Attractor.

Symmetry The Poincaré Map has an Inversion Symmetry such that In The PFP, The Poincaré Map and flow has an Inversion Symmetry and Asymmetry. Inversion Symmetry Inversion Asymmetry

Summary 1. A dynamical system is described by differential equation mathematically. 2. The Poincaré Map(T) is Convenient for Finding The Periodic Orbit, Analyzing the Stability of The Orbit, Showing up Fractal Geometric Properties of Attractor.