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| Preface | |
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| Newton's Laws for Particles and Rigid Bodies | |
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| Newton's Second Law | |
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| Coordinate Frames and Velocity and Acceleration Diagrams | |
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| Rectangular Coordinates | |
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| Polar Coordinates | |
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| Coordinate Choice and Degrees-of-Freedom | |
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| Free-Body and Force Diagrams | |
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| Transferring Velocity and Acceleration Components | |
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| Transferring Motion Components of Rigid Bodies and Generating Kinematic Constraints | |
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| Kinematic Constraints | |
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| Review of Center of Mass, Linear Momentum, and Angular Momentum for Rigid Bodies | |
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| Newton's Law Applied to Rigid Bodies | |
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| Reference | |
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| Problems | |
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| Equations of Motion in Second- and First-Order Form | |
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| Deriving Equations of Motion for Systems of Particles | |
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| Deriving Equations of Motion When Rigid Bodies Are Part of the System | |
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| Forms of Equations and Their Computational Solution | |
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| First-Order State Equations | |
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| Explicit Form | |
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| Fundamentals of Computer-Developed Time-Step Simulation | |
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| Implicit Form | |
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| Differential Algebraic Form | |
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| Reducing Sets of Second-Order Differential Equations to First-Order Form | |
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| Matrix Forms for Linearized Equations | |
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| Quarter-Car Model for Vibration Analysis | |
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| Half-Car Model for Vibration Analysis and Control | |
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| Linearization of the Inverted Pendulum | |
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| Summary | |
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| References | |
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| Problems | |
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| Computer Solution of Equations of Motion | |
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| Time-Step Simulation of Nonlinear-Equations of Motion | |
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| Linear System Response | |
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| Eigenvalues and Their Relationship to System Stability | |
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| Transfer Functions | |
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| Frequency Response | |
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| References | |
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| Problems | |
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| Energy and Lagrange Equation Methods | |
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| Kinetic and Potential Energy | |
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| Using Conservation of Energy to Derive Equations of Motion | |
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| Equations of Motion from Lagrange's Equations | |
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| Generalized Coordinates | |
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| Lagrange's Equations | |
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| Generalized Forces | |
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| Imposed Motion | |
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| Interpretation of Lagrange's Equations | |
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| Nonlinear Kinematics and Lagrange's Equations | |
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| Approximate Method for Satisfying Constraints | |
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| First-Order Forms for Lagrange's Equations | |
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| Example System | |
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| Comments Regarding the Use of p and q Variables in Simulation | |
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| Nonholonomic Systems | |
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| Summary | |
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| References | |
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| Problems | |
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| Newton's Laws in a Body-Fixed Frame: Application to Vehicle Dynamics | |
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| The Dynamics of a Shopping Cart | |
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| Inertial Coordinate System | |
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| Body-Fixed Coordinate System | |
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| Connection between Inertial and Body-Fixed Frames | |
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| Analysis of a Simple Car Model | |
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| Vehicle Stability | |
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| Stability, Critical Speed, Understeer, and Oversteer | |
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| Steering Transfer Functions | |
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| Yaw Rate and Lateral Acceleration Gains | |
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| Special Case of the Neutral Steering Vehicle | |
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| Steady Cornering | |
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| Description of Steady Turns | |
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| Significance of the Understeering Coefficient | |
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| Acceleration and Yaw Rate Gain Behavior | |
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| Summary | |
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| References | |
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| Problems | |
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| Mechanical Systems under Active Control | |
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| Basic Concepts | |
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| Characteristic Equation | |
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| Transfer Functions | |
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| State-Variable Feedback | |
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| State Variables and Active Control | |
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| Compromises in Passive Vibration Isolation | |
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| Active Control in Vibration Isolation | |
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| Optimized Active Vibration Isolator | |
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| Steering Control of Banking Vehicles | |
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| Development of the Mathematical Model | |
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| Derivation of the Dynamic Equations | |
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| Stability of the Lean Angle | |
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| Steering Control of the Lean Angle | |
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| Counter Steering or Reverse Action | |
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| Active Control of Vehicle Dynamics | |
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| Stability and Control | |
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| From ABS to VDC | |
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| Model Reference Control | |
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| Active Steering Systems | |
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| Stability Augmentation Using Front, Rear, or All-Wheel Steering | |
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| Feedback Model Following Active Steering Control | |
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| Sliding Mode Control | |
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| Active Steering Applied to the Bicycle Model of an Automobile | |
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| Active Steering Yaw Rate Controller | |
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| Limitations of Active Stability Enhancement | |
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| Summary | |
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| References | |
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| Problems | |
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| Rigid-Body Motion in Three Dimensions | |
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| General Equations of Motion | |
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| Use of a Body-Fixed Coordinate Frame | |
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| Euler's Equations | |
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| Spin Stabilization of Satellites | |
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| Use of an Inertial Coordinate Frame | |
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| Euler's Angles | |
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| Kinetic Energy | |
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| Steady Precession of Gyroscopes | |
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| Dynamics of Gyroscopes | |
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| Summary | |
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| References | |
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| Problems | |
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| Vibration of Multiple-Degree-of-Freedom Systems | |
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| Natural Frequency and Resonance of a Single-Degree-of-Freedom Oscillator | |
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| Free Response | |
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| Forced Response | |
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| Comparison of Two Suspension Geometries | |
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| Two-Degree-of-Freedom Systems | |
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| Free, Undamped Response | |
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| Forced Response of Two-Degree-of-Freedom Systems | |
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| Tuned Vibration Absorbers | |
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| Some Configurations for TVAs | |
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| Summary | |
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| References | |
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| Problems | |
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| Distributed System Vibrations | |
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| Stress Waves in a Rod | |
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| Free Response: Separation of Variables | |
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| Forced Response | |
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| Orthogonality of Mode Functions | |
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| Representation of Point Forces | |
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| Rigid-Body Mode | |
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| Back to the Forced Response | |
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| Attaching the Distributed System to External Dynamic Components | |
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| Tightly Stretched Cable | |
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| Free Response: Separation of Variables | |
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| Forced Response | |
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| Bernoulli-Euler Beam | |
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| Free Response: Separation of Variables | |
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| Forced Response | |
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| Summary | |
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| References | |
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| Problems | |
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| Three-Dimensional Rigid-Body Motion in a Rotating Coordinate System | |
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| References | |
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| Moments of Inertia for Some Common Body Shapes | |
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| Parallel Axis Theorem | |
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| Index | |