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