A Practical Approach to Dynamical Systems for Engineers.

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 -- REFERENCES -- FURTHER READING -- 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 -- REFERENCES -- 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 -- REFERENCES -- FURTHER READING -- 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 -- REFERENCES -- FURTHER READING -- INDEX -- A -- B -- C -- D -- E -- F -- H -- I -- J -- L -- M -- N -- O -- P -- S -- T -- U -- Z -- Back Cover.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.