A practical approach to dynamical systems for engineers / Patricia Mellodge.

Format:

Book

Author/Creator:

Mellodge, Patricia, author.

Series:

Woodhead Publishing in mechanical engineering.

Woodhead publishing series in mechanical engineering

Language:

English

Subjects (All):

Dynamics.

Mechanics, Applied.

Physical Description:

1 online resource (294 p.)

Edition:

1st ed.

Place of Publication:

Amsterdam : Elsevier : Woodhead Publishing, [2016]

Summary:

A Practical Approach to Dynamical Systems for Engineers takes the abstract mathematical concepts behind dynamical systems and applies them to real-world systems, such as a car traveling down the road, the ripples caused by throwing a pebble into a pond, and a clock pendulum swinging back and forth.Many relevant topics are covered, including modeling systems using differential equations, transfer functions, state-space representation, Hamiltonian systems, stability and equilibrium, and nonlinear system characteristics with examples including chaos, bifurcation, and limit cycles.In addition, MATLAB is used extensively to show how the analysis methods are applied to the examples. It is assumed readers will have an understanding of calculus, differential equations, linear algebra, and an interest in mechanical and electrical dynamical systems.- Presents applications in engineering to show the adoption of dynamical system analytical methods- Provides examples on the dynamics of automobiles, aircraft, and human balance, among others, with an emphasis on physical engineering systems- MATLAB and Simulink are used throughout to apply the analysis methods and illustrate the ideas- Offers in-depth discussions of every abstract concept, described in an intuitive manner, and illustrated using practical examples, bridging the gap between theory and practice- Ideal resource for practicing engineers who need to understand background theory and how to apply it

Contents:

Front Cover

A Practical Approach to Dynamical Systems for Engineers

Copyright

CONTENTS

LIST OF FIGURES

LIST OF TABLES

ABOUT THE AUTHOR

PREFACE

1 - Introduction: What Is a Dynamical System?

1.1 OVERVIEW

1.1.1 Why Do We Study Dynamic Systems?

1.2 TYPES OF SYSTEMS

1.2.1 Continuous versus Discrete

1.2.2 Linear versus Nonlinear

1.2.3 Time-Invariant versus Time-Varying

1.2.4 Memory versus Memoryless

1.2.5 Causal versus Noncausal

1.2.6 Deterministic versus Stochastic

1.3 EXAMPLES OF DYNAMICAL SYSTEMS

1.4 A NOTE ON MATLAB AND SIMULINK

REFERENCES

FURTHER READING

2 - System Modeling

2.1 INTRODUCTION

2.2 EQUATIONS OF MOTION

2.2.1 Differential Equations for Continuous-Time Systems

2.2.1.1 MATLAB Example: Car Suspension

2.2.1.2 Simulink Example: Kinematic Car Model

2.2.2 Difference Equations for Discrete-Time Systems

2.2.2.1 MATLAB Example: Bank Account with Interest

2.2.3 Models for Hybrid Systems

2.2.3.1 MATLAB Example: Computer-Controlled Vehicle Dynamics

2.2.4 Flows, Vector Fields, and the Phase Plane

2.2.4.1 MATLAB Example: Phase Plot of a Pendulum

2.3 TRANSFER FUNCTIONS

2.3.1 Overview

2.3.2 Laplace Transforms for Continuous-Time Systems

2.3.2.1 MATLAB Example: Transfer Function for the Car Suspension

2.3.2.2 MATLAB Example: Transfer Function of the Human Balance System

2.3.2.3 Systems with Nonzero Initial Conditions

2.3.3 z-Transforms for Discrete-Time Systems

2.3.3.1 MATLAB Example: Model of a Computer-Controlled Heating System

2.4 STATE-SPACE REPRESENTATION

2.4.1 Overview

2.4.2 What Is a State?

2.4.2.1 MATLAB Example: State-Space Model of the Car Suspension

2.4.2.2 MATLAB Example: Alternate State-Space Model of the Car Suspension

2.4.2.3 MATLAB Example: System with Nonzero Initial Conditions.

2.4.3 Relationship between Transfer Functions and State-space Models

2.4.3.1 MATLAB Example: Converting a State-Space Model to a Transfer Function for a Hanging Crane

2.4.4 Canonical Forms

2.4.4.1 Controllable Canonical Form

2.4.4.2 Observable Canonical Form

2.4.4.3 Phase Variable Canonical Form

2.4.4.4 Modal (or Diagonal) Canonical Form

2.4.4.5 Jordan Canonical Form

2.4.4.6 Chained Form

2.4.4.7 Application Examples

2.4.5 Eigenvalues and Eigenvectors

2.4.5.1 MATLAB Example: Eigenvalues and Eigenvectors of the Pendulum

2.4.6 Singular Value Decomposition

2.4.6.1 MATLAB Example: Inverse Kinematics of the Robotic Arm

2.4.6.2 MATLAB Example: Manipulability Ellipse of the Robotic Arm

2.5 SYSTEM IDENTIFICATION

2.5.1 Overview

2.5.2 Case Study: Human Balance Model

3 - Characteristics of Dynamical Systems

3.1 OVERVIEW

3.2 EXISTENCE AND UNIQUENESS OF SOLUTIONS: WHY IT MATTERS

3.2.1 What Is a Solution?

3.2.2 Existence and Uniqueness Theorem

3.2.3 Application Examples

3.2.4 Solutions of Linear Systems

3.3 EQUILIBRIUM AND NULLCLINES

3.3.1 Population Dynamics

3.3.1.1 MATLAB Example: Predator-Prey System Phase Plot

3.3.2 Double Pendulum

3.4 STABILITY

3.4.1 Stable Systems

3.4.1.1 Spectral Stability

3.4.1.2 Linear Stability

3.4.1.3 Asymptotic Linear Stability

3.4.2 Stable Equilibrium Points

3.4.2.1 Lyapunov Stability

3.4.2.2 Asymptotic Stability

3.4.2.3 Exponential Stability

3.4.2.4 Instability

3.4.2.5 Marginal Stability

3.4.3 Stable Responses to an Input

3.4.3.1 BIBO Stability

3.4.3.2 BIBS Stability

3.4.4 Relationship between Types of Stability

3.4.5 Examples

3.4.5.1 MATLAB Example: Pendulum Stability

3.4.5.2 MATLAB Example: Motor Positioning System

3.4.5.3 MATLAB Example: Mechanical Belt.

3.4.5.4 Example: Automobile Longitudinal Dynamics

3.5 LYAPUNOV FUNCTIONS

3.5.1 Lyapunov Functions for Linear Systems

3.5.1.1 MATLAB Example: Lyapunov Function for a Linearized Pendulum

3.5.2 Method of Gradients

3.5.2.1 Example: Lyapunov Function for the Pendulum

4 - Characteristics of Nonlinear Systems

4.1 TYPES OF NONLINEAR SYSTEMS

4.1.1 Relay

4.1.2 Saturation

4.1.3 Dead Zone

4.1.4 Coulomb and Viscous Friction

4.1.5 Hysteresis

4.2 LIMIT CYCLES

4.2.1 Simulink Example: Limit Cycles in a Jet Engine Control System

4.3 BIFURCATION

4.3.1 Example: Bifurcation in the Logistic Differential Equation

4.3.2 MATLAB Example: Bifurcation in the Mechanical Belt System

4.4 CHAOS

4.4.1 Example: Chaotic Behavior in the Logistic Equation

4.4.2 MATLAB Example: Using Chaos to Control a Mobile Robot

4.5 LINEARIZATION

4.5.1 Linearization Using Taylor Series Expansion

4.5.1.1 Example: Linearizing the Pendulum

4.5.1.2 Example: Linearizing a Friction Function

4.5.2 Linearization and Stability

4.5.3 Feedback Linearization

4.5.3.1 Example: Input-State Linearization of the Pendulum

4.5.3.2 Example: Input-Output Linearization of a Field-Controlled Direct Current Motor

5 - Hamiltonian Systems

5.1 OVERVIEW

5.2 STRUCTURE OF HAMILTONIAN SYSTEMS

5.3 EXAMPLES

5.3.1 Harmonic Oscillator

5.3.2 Pendulum

5.3.3 Population Dynamics

5.3.4 Chaplygin Sleigh

5.4 CONCLUSION

INDEX

A

B

C

D

E

F

H

I

J

L

M

N

O

P

S

T

U

Z

Back Cover.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed December 31, 2015).

ISBN:

9780081002247

0081002246

OCLC:

932333165