An Introduction to Phase Space

4/15/99


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Table of Contents

An Introduction to Phase Space

Contents

Introduction

Assumptions & Implications

Phase Space

Flow in Phase Space

Equivalent First Order System

PPT Slide

Picard’s Theorem

PPT Slide

Autonomous Systems

PPT Slide

PPT Slide

PPT Slide

Separation of Variables

PPT Slide

Fixed Points

PPT Slide

PPT Slide

PPT Slide

PPT Slide

PPT Slide

PPT Slide

Center Example

Center Example Animation

Sink Example

Sink Example Animation

Source Example

Source Example Animation

Saddle Example

Saddle Example Animation

Non-Autonomous Systems

PPT Slide

PPT Slide

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

PPT Slide

The Undamped Pendulum

Fixed Points

First Integral of Motion

The Separatrix

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

Using MPP

Using Maple

Further Topics

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