Engineering Applications of Dynamics / Edition 1

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Designed to address the perceived failure of introductory dynamics courses to produce students capable of applying dynamic principles successfully, both in subsequent courses and in practice, Engineering Applications of Dynamics adopts a much-needed practical approach designed to make the subject not only more relevant, but more interesting as well.

Written by a highly respected team of authors, the book is the first of its kind to tie dynamics theory directly to real-world situations. By touching on complex concepts only to the extent of illustrating their value in real-world applications, the authors provide students with a deeper understanding of dynamics in the engineering of mechanical systems.

Topics of interest include:
* The formulation of equations in forms suitable for computer simulation
* Simulation examples of real engineering systems
* Applications to vehicle dynamics
* Lagrange's equations as an alternative formulation procedure
* Vibrations of lumped and distributed systems
* Three-dimensional motion of rigid bodies, with emphasis on gyroscopic effects
* Transfer functions for linearized dynamic systems
* Active control of dynamic systems

A Solutions Manual with detailed solutions for al problems in this book is available at the Web site,

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Product Details

  • ISBN-13: 9780470112663
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 12/21/2007
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 432
  • Sales rank: 498,932
  • Product dimensions: 6.46 (w) x 9.41 (h) x 1.12 (d)

Meet the Author

Dean C. Karnopp and Donald L. Margolis are professors of mechanical engineering at the University of California, Davis.

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Table of Contents

Preface     xi
Newton's Laws for Particles and Rigid Bodies     1
Newton's Second Law     2
Coordinate Frames and Velocity and Acceleration Diagrams     3
Rectangular Coordinates     3
Polar Coordinates     4
Coordinate Choice and Degrees-of-Freedom     8
Free-Body and Force Diagrams     9
Transferring Velocity and Acceleration Components     11
Transferring Motion Components of Rigid Bodies and Generating Kinematic Constraints     16
Kinematic Constraints     18
Review of Center of Mass, Linear Momentum, and Angular Momentum for Rigid Bodies     21
Newton's Law Applied to Rigid Bodies     25
Reference     27
Problems     27
Equations of Motion in Second- and First-Order Form     41
Deriving Equations of Motion for Systems of Particles     41
Deriving Equations of Motion When Rigid Bodies Are Part of the System     46
Forms of Equations and Their Computational Solution     55
First-Order State Equations     56
Explicit Form     56
Fundamentals of Computer-Developed Time-Step Simulation     57
Implicit Form     57
Differential Algebraic Form     58
Reducing Sets of Second-Order Differential Equations to First-Order Form     58
Matrix Forms for Linearized Equations     64
Quarter-Car Model for Vibration Analysis     64
Half-Car Model for Vibration Analysis and Control     68
Linearization of the Inverted Pendulum     71
Summary     73
References     74
Problems     74
Computer Solution of Equations of Motion     92
Time-Step Simulation of Nonlinear-Equations of Motion     92
Linear System Response     107
Eigenvalues and Their Relationship to System Stability     107
Transfer Functions     110
Frequency Response     114
References     118
Problems     119
Energy and Lagrange Equation Methods     135
Kinetic and Potential Energy     136
Using Conservation of Energy to Derive Equations of Motion     139
Equations of Motion from Lagrange's Equations     141
Generalized Coordinates     141
Lagrange's Equations     144
Generalized Forces     146
Imposed Motion     148
Interpretation of Lagrange's Equations     150
Nonlinear Kinematics and Lagrange's Equations     152
Approximate Method for Satisfying Constraints     156
First-Order Forms for Lagrange's Equations     158
Example System     160
Comments Regarding the Use of p and q Variables in Simulation     161
Nonholonomic Systems     162
Summary     162
References     163
Problems     163
Newton's Laws in a Body-Fixed Frame: Application to Vehicle Dynamics     180
The Dynamics of a Shopping Cart     181
Inertial Coordinate System     181
Body-Fixed Coordinate System     187
Connection between Inertial and Body-Fixed Frames     189
Analysis of a Simple Car Model     190
Vehicle Stability     193
Stability, Critical Speed, Understeer, and Oversteer     196
Steering Transfer Functions     197
Yaw Rate and Lateral Acceleration Gains     200
Special Case of the Neutral Steering Vehicle     200
Steady Cornering     202
Description of Steady Turns     202
Significance of the Understeering Coefficient     204
Acceleration and Yaw Rate Gain Behavior     205
Summary     209
References      209
Problems     209
Mechanical Systems under Active Control     219
Basic Concepts     220
Characteristic Equation     221
Transfer Functions     221
State-Variable Feedback     222
State Variables and Active Control     222
Compromises in Passive Vibration Isolation     224
Active Control in Vibration Isolation     226
Optimized Active Vibration Isolator     228
Steering Control of Banking Vehicles     231
Development of the Mathematical Model     232
Derivation of the Dynamic Equations     234
Stability of the Lean Angle     237
Steering Control of the Lean Angle     238
Counter Steering or Reverse Action     240
Active Control of Vehicle Dynamics     242
Stability and Control     243
From ABS to VDC     244
Model Reference Control     246
Active Steering Systems     248
Stability Augmentation Using Front, Rear, or All-Wheel Steering     249
Feedback Model Following Active Steering Control     249
Sliding Mode Control     251
Active Steering Applied to the Bicycle Model of an Automobile      254
Active Steering Yaw Rate Controller     256
Limitations of Active Stability Enhancement     260
Summary     261
References     261
Problems     262
Rigid-Body Motion in Three Dimensions     271
General Equations of Motion     272
Use of a Body-Fixed Coordinate Frame     275
Euler's Equations     276
Spin Stabilization of Satellites     277
Use of an Inertial Coordinate Frame     281
Euler's Angles     283
Kinetic Energy     285
Steady Precession of Gyroscopes     285
Dynamics of Gyroscopes     287
Summary     292
References     293
Problems     293
Vibration of Multiple-Degree-of-Freedom Systems     305
Natural Frequency and Resonance of a Single-Degree-of-Freedom Oscillator     306
Free Response     306
Forced Response     309
Comparison of Two Suspension Geometries     309
Two-Degree-of-Freedom Systems     314
Free, Undamped Response     315
Forced Response of Two-Degree-of-Freedom Systems     326
Tuned Vibration Absorbers     328
Some Configurations for TVAs     332
Summary     339
References     339
Problems     340
Distributed System Vibrations     350
Stress Waves in a Rod     350
Free Response: Separation of Variables     354
Forced Response     357
Orthogonality of Mode Functions     359
Representation of Point Forces     359
Rigid-Body Mode     362
Back to the Forced Response     363
Attaching the Distributed System to External Dynamic Components     366
Tightly Stretched Cable     372
Free Response: Separation of Variables     375
Forced Response     377
Bernoulli-Euler Beam     379
Free Response: Separation of Variables     382
Forced Response     384
Summary     388
References     389
Problems     389
Three-Dimensional Rigid-Body Motion in a Rotating Coordinate System     402
References     407
Moments of Inertia for Some Common Body Shapes     408
Parallel Axis Theorem     410
Index     413
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