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Table of Contents Preface Chapter 1 Newton?s Laws for Particles and Rigid bodies 1.1 Newton?s 2nd Law 1.2 Coordinate Frames, Velocity and Acceleration Diagrams Choosing coordinates, Degrees-of-Freedom 1.3 Free Body diagrams and Force Diagrams 1.4 Transferring Velocity and Acceleration Components 1.5 Transferring Motion Components of Rigid Bodies and Generating Kinematic Constraints Kinematic constraints 1.6 Review of Center of Mass, Linear Momentum, and Angular Momentum for Rigid Bodies 1.7 Newton?s law Applied to Rigid Bodies 1.8 References Chapter 2 Equations of Motion in Second and First Order Form Deriving Equations of Motion Using Newton?s Laws 2.1 Deriving Equations of Motion for Systems of Particles Example 1-Spring Pendulum Example 2-Spring Pendulum Attached to a Cart 2.2 Deriving Equations of Motion When Rigid Bodies are Part of the System Example 3-Pinned Disk with a Slot and Mass Particle Example 4-Cart with Rigid Body Pendulum Example 5-Slider Crank System 2.3 Forms of Equations and their Computational Solution First Order State Equations Explicit Form The fundamentals of how computers march out time-step simulation Implicit Form Differential Algebraic Form 2.4 Reducing Sets of Second Order Differential Equations to First Order Form Example 1-Spring Pendulum Example 2 ?Spring Pendulum Attached to a Cart Example 3-Pinned Disk with a Slot and Mass Particle Example 4-Inverted Rigid Body Pendulum on a Cart 2.5 Matrix Forms for Linearized Equations Quarter Car Model for Vibration Analysis Half Car Model for Vibration Analysis and Control Linearization of the Inverted Pendulum 2.6 Summary 2.7 References Chapter 3 Computer Solution of Equations of Motion 3.1 Time Step Simulation of Nonlinear Equations of Motion Simulation Example 1-Spring Pendulum Simulation Example 2- Pinned Disk with a Slot and Mass Particle Simulation Example 3-Stabilizing an Inverted Pendulum 3.2 Linear System Response Eigenvalues and Their Relationship to System Stability Transfer Functions Frequency Response 3.3 References Chapter 4 Energy and Lagrange Equation Methods 4.1 Kinetic and Potential Energy 4.2 Using Conservation of Energy to Derive Equations of Motion 4.3 Equations of Motion from Lagrange?s Equations Generalized Coordinates Equations of Motion Lagrange?s Equations Generalized Forces Imposed Motion 4.4 Interpretation of Lagrange?s Equations 4.5 Nonlinear Kinematics and Lagrange?s Equations Example 1 Example 2 Example 3 An Approximate Method for Satisfying Constraints 4.6 First Order Forms for Lagrange?s Equations An Example System Chapter 5 Newton?s Laws in a Body-Fixed Frame: Application to Vehicle Dynamics 5.1 The Dynamics of a Shopping Cart Inertial Coordinate System Body-Fixed Coordinate System The Connection between Inertial and Body-Fixed Frames 5.2 Analysis of a Simple Car Model 5.3 Vehicle Stability 5.4 Stability, Critical Speed, Understeer and Oversteer 5.5 Steering Transfer Functions Yaw Rate and Lateral Acceleration Gains The Special Case of a Neutral Steer Vehicle 5.6 Steady Cornering Description of Steady Turns Significance of the Understeer Coefficient Acceleration and Yaw Rate Gain Behavior 5.7 Summary 5.8 References Chapter 6 Mechanical systems under Active Control 6.1 Basic Concepts The Characteristic Equation Transfer Functions State Variable Feedback 6.2 State Variables and Active Control Compromises in Passive Vibration Isolation Active Control in Vibration Isolation Optimized Active Vibration Isolator 6.3 Steering Control of Banking Vehicles Development of the Mathematical Model Derivation of the Dynamic Equations Stability of the Lean Angle Steering Control of the Lean Angle Counter Steering or Reverse Action 6.4 Active Control of Vehicle Dynamics Stability and Control From ABS to VDC Model Reference Control Active Steering Systems Stability Augmentation Using Front, Rear or All Wheel Steering Feedback Model Following Active Steering Control Sliding Mode Control Active Steering Applied to the Bicycle Model of an Automobile Active Steering Yaw Rate Controller Limitations of Active Stability Enhancement 6.5 Summary 6.6 References Chapter 7 Rigid Body Motion in Three Dimensions 7.1 The General Equations of Motion 7.2 Use of a Body-Fixed Coordinate Frame Euler?s Equations Spin Stabilization of Satellites 7.3 Use of an Inertial Coordinate Frame Euler?s Angles Kinetic Energy Steady Precession of Gyroscopes Dynamics of Gyroscopes 7.4 Summary 7.5 References Chapter 8 Vibration of Multiple Degree-Of-Freedom Systems 8.1 Natural Frequency and Resonance of a One D-O-F Oscillator Free Response Forced Response Comparison of Two Suspension Geometries 8.2 Two Degree-of-Freedom Systems Free, Undamped Response Forced Response of Two Degree-Of-Freedom Systems 8.3 Tuned Vibration Absorbers Some Configurations for TVA?s 8.4 Summary 8.5 References Chapter 9 Distributed System Vibrations 9.1 Stress Waves in a Rod Free Response, Separation of Variables Forced Response Orthogonality of Mode Functions Representation of Point Forces Rigid Body Mode Back to Forced Response 9.2 Attaching the Distributed System to External Dynamic Components 9.3 Tightly Stretched Cable Free Response, Separation of Variables Forced Response 9.4 Bernoulli-Euler Beam Free Response, Separation of Variables Forced Response 9.5 Summary 9.6 References Appendix 1 Three-Dimensional Rigid Body in a Rotating Coordinate System Appendix 2 Moments of Inertia for Some Common Body Shapes Appendix 3 The Parallel Axis Theorem Index
Library of Congress Subject Headings for this publication:
Structural dynamics.
Structural engineering.