- Presents an easy, step-by-step introduction to simulating dynamics
- Uses the student version of Simulink for constructing simulations
- Requires no general-purpose programming skills
- Includes a wide range of examples and exercises from the areas of physics, biology, economics, mathematics, and engineering
- Provides PowerPoint slides and solutions to exercises at http://nw08.american.edu/~gray

Designed for undergraduate students in the general science, engineering, and mathematics community, **Introduction to the Simulation of Dynamics Using Simulink ^{®}** shows how to use the powerful tool of Simulink to investigate and form intuitions about the behavior of dynamical systems. Requiring no prior programming experience, it clearly explains how to transition from physical models described by mathematical equations directly to executable Simulink simulations.

*Teaches students how to model and explore the dynamics of systems*Step by step, the author presents the basics of building a simulation in Simulink. He begins with finite difference equations and simple discrete models, such as annual population models, to introduce the concept of state. The text then covers ordinary differential equations, numerical integration algorithms, and time-step simulation. The final chapter offers overviews of some advanced topics, including the simulation of chaotic dynamics and partial differential equations.

*A one-semester undergraduate course on simulation*Written in an informal, accessible style, this guide includes many diagrams and graphics as well as exercises embedded within the text. It also draws on numerous examples from the science, engineering, and technology fields. The book deepens students’ understanding of simulated systems and prepares them for advanced and specialized studies in simulation. Ancillary materials are available at http://nw08.american.edu/~gray

**Introduction and Motivation**

Systems

Dynamical Models of Physical Systems

Constructing Simulations from Dynamical Models

How Simulators Are Used

**The Basics of Simulation in Simulink**Simplest Model to Simulate

Models in Simulink

Simulation of the Simplest Model

Understanding How Time Is Handled in Simulation

A Model with Time as a Variable

How Simulink Propagates Values in Block Diagrams

A Model with Uniform Circular Motion

A Model with Spiraling Circular Motion

Uncertainty in Numbers and Significant Figures

**Simulation of First-Order Difference Equation Models**

What Is a Difference Equation?

Examples of Systems with Difference Equation Models

First-Order Difference Equation Simulation

Examining the Internals of a Simulation

Organizing the Internal Structure of a Simulation

Using Vector and Matrix Data

**Simulation of First-Order Differential Equation Models**

What Is a Differential Equation?

Examples of Systems with Differential Equation Models

Reworking First-Order Differential Equations into Block Form

First-Order Differential Equation Simulation

Saving Simulation Data in MATLAB

**Fixed-Step Solvers and Numerical Integration Methods**

What Is a Solver?

Understanding the Basics of Numerical Integration Algorithms

Understanding Solver Errors

Improving the Basic Algorithms

Fixed-Step Solvers in the Simulink Software

**Simulation of First-Order Equation Systems**

What Is a First-Order Difference Equation System?

Examples of First-Order Difference Equation Systems

Simulating a First-Order Difference Equation System

What Is a First-Order Differential Equation System?

Examples of First-Order Differential Equation Systems

Simulating a First-Order Differential Equation System

Combining Connections on a Bus

**Simulation of Second-Order Equation Models: Nonperiodic Dynamics**

Simulation of Second-Order Difference Equation Models

Simulation of Second-Order Differential Equation Models

Second-Order Differential Equation Models with First-Order Terms

Conditional Dynamics

**Simulation of Second-Order Equation Models: Periodic Dynamics**

Orbital Systems

Masked Subsystems

Creating Libraries

**Higher-Order Models and Variable-Step Solvers **Direct Simulation by Multiple Integrations

Producing Function Forms for Simulation Results

Variable-Step Solvers

Variable-Step Solvers in Simulink

**Advanced Topics: Transforming Ordinary Differential Equations, Simulation of Chaotic Dynamics, and Simulation of Partial Differential Equations**

Transforming Ordinary Differential Equations

Simulation of Chaotic Dynamics

Simulation of Partial Differential Equations

**Appendix A: Alphabetical List of Simulink BlocksAppendix B: The Basics of MATLAB for Simulink UsersAppendix C: Debugging a Simulink Model**

**Index**

*A Summary, References, and Additional Reading appear at the end of each chapter.*

**Michael A. Gray** is an associate professor in the Department of Computer Science at American University in Washington, D.C.