An Introduction to Phase Space

4/15/99

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Table of Contents

An Introduction to Phase Space

Assumptions & Implications

Flow in Phase Space

Equivalent First Order System

Picard’s Theorem

Autonomous Systems

Separation of Variables

Center Example Animation

Sink Example Animation

Source Example Animation

Saddle Example Animation

Non-Autonomous Systems

Non-Autonomous Examples

Non-Autonomous Example 1

Example 1 Animation

Non-Autonomous Example 2

Example 2 Animation

The Simple Pendulum

Forces on the Weight

The Differential Equation

The Undamped Pendulum

First Integral of Motion

Phase Space Portrait of The Undamped Simple Pendulum

The Damped Simple Pendulum

Phase Space Portrait of The Damped Simple Pendulum

Phase and Real Space Orbits of the Simple Pendulum

Making Phase Space Orbits

Simple Non-Linear Example

Dynamical Systems

Islands of Stability

Chaos Looking You in the Face

Undamped Simple Pendulum

Damped Simple Pendulum

Author: Al Lehnen

Email: aplehnen@execpc.com

Home Page: www.execpc.com/~aplehnen/al