Intermediate Dynamics for Engineers: A Unified Treatment of Newton-Euler and Lagrangian Mechanics

by Oliver M. O'Reilly

• ISBN13: 9780521874830
• ISBN10: 0521874831
• Format: Hardcover
• Copyright: 2008-08-04
• Publisher: Cambridge University Press

Summary

This book has sufficient material for two semester-length courses in intermediate engineering dynamics. For the first course, a Newton-Euler approach is used, followed by a Lagrangrian approach in the second. Using some ideas from differential geometry, the equivalence of these two approaches is illuminated throughout the text. In addition, this book contains comprehensive treatments of the kinematics and dynamics of particles and rigid bodies. The subject matter is illuminated by numerous, highly structured examples and exercises featuring a wide range of applications and numerical simulations.

Author Biography

Oliver M. O'Reilly is a professor of mechanical engineering at the University of California, Berkeley. His research interests lie in continuum mechanics and nonlinear dynamics, specifically in the dynamics of rigid bodies and particles, Cosserat and directed continuua, dynamics of rods, history of mechanics, and vehicle dynamics. O'Reilly is the author of more than 50 archival publications and Engineering Dynamics: A Primer. He is also the recipient of the University of California at Berkeley's Distinguished Teaching Award and three departmental teaching awards

Table of Contents

Preface	p. xi
Dynamics of a Single Particle	p. 1
Kinematics of a Particle	p. 3
Introduction	p. 3
Reference Frames	p. 3
Kinematics of a Particle	p. 5
Frequently Used Coordinate Systems	p. 6
Curvilinear Coordinates	p. 9
Representations of Particle Kinematics	p. 14
Constraints	p. 15
Classification of Constraints	p. 20
Closing Comments	p. 27
Exercises	p. 27
Kinetics of a Particle	p. 33
Introduction	p. 33
The Balance Law for a Single Particle	p. 33
Work and Power	p. 35
Conservative Forces	p. 36
Examples of Conservative Forces	p. 37
Constraint Forces	p. 39
Conservations	p. 45
Dynamics of a Particle in a Gravitational Field	p. 47
Dynamics of a Particle on a Spinning Cone	p. 55
A Shocking Constraint	p. 59
A Simple Model for a Roller Coaster	p. 60
Closing Comments	p. 64
Exercises	p. 66
Lagrange's Equations of Motion for a Single Particle	p. 70
Introduction	p. 70
Lagrange's Equations of Motion	p. 71
Equations of Motion for an Unconstrained Particle	p. 73
Lagrange's Equations in the Presence of Constraints	p. 74
A Particle Moving on a Sphere	p. 78
Some Elements of Geometry and Particle Kinematics	p. 80
The Geometry of Lagrange's Equations of Motion	p. 83
A Particle Moving on a Helix	p. 87
Summary	p. 91
Exercises	p. 92
Dynamics of a System of Particles	p. 101
The Equations of Motion for a System of Particles	p. 103
Introduction	p. 103
A System of N Particles	p. 104
Coordinates	p. 105
Constraints and Constraint Forces	p. 107
Conservative Forces and Potential Energies	p. 110
Lagrange's Equations of Motion	p. 111
Construction and Use of a Single Representative Particle	p. 113
The Lagrangian	p. 118
A Constrained System of Particles	p. 119
A Canonical Form of Lagrange's Equations	p. 122
Alternative Principles of Mechanics	p. 128
Closing Remarks	p. 131
Exercises	p. 131
Dynamics of Systems of Particles	p. 134
Introduction	p. 134
Harmonic Oscillators	p. 134
A Dumbbell Satellite	p. 140
A Pendulum and a Cart	p. 143
Two Particles Tethered by an Inextensible String	p. 147
Closing Comments	p. 151
Exercises	p. 153
Dynamics of a Single Rigid Body	p. 161
Rotation Tensors	p. 163
Introduction	p. 163
The Simplest Rotation	p. 164
Proper-Orthogonal Tensors	p. 166
Derivatives of a Proper-Orthogonal Tensor	p. 168
Euler's Representation of a Rotation Tensor	p. 171
Euler's Theorem: Rotation Tensors and Proper-Orthogonal Tensors	p. 176
Relative Angular Velocity Vectors	p. 178
Euler Angles	p. 181
Further Representations of a Rotation Tensor	p. 191
Derivatives of Scalar Functions of Rotation Tensors	p. 195
Exercises	p. 198
Kinematics of Rigid Bodies	p. 206
Introduction	p. 206
The Motion of a Rigid Body	p. 206
The Angular Velocity and Angular Acceleration Vectors	p. 211
A Corotational Basis	p. 212
Three Distinct Axes of Rotation	p. 213
The Center of Mass and Linear Momentum	p. 215
Angular Momenta	p. 218
Euler Tensors and Inertia Tensors	p. 219
Angular Momentum and an Inertia Tensor	p. 223
Kinetic Energy	p. 224
Concluding Remarks	p. 226
Exercises	p. 226
Constraints on and Potentials for Rigid Bodies	p. 237
Introduction	p. 237
Constraints	p. 237
A Canonical Function	p. 241
Integrability Criteria	p. 243
Forces and Moments Acting on a Rigid Body	p. 247
Constraint Forces and Constraint Moments	p. 248
Potential Energies and Conservative Forces and Moments	p. 256
Concluding Comments	p. 262
Exercises	p. 263
Kinetics of a Rigid Body	p. 272
Introduction	p. 272
Balance Laws for a Rigid Body	p. 272
Work and Energy Conservation	p. 274
Additional Forms of the Balance of Angular Momentum	p. 276
Moment-Free Motion of a Rigid Body	p. 279
The Baseball and the Football	p. 285
Motion of a Rigid Body with a Fixed Point	p. 289
Motions of Rolling Spheres and Sliding Spheres	p. 294
Closing Comments	p. 297
Exercises	p. 299
Lagrange's Equations of Motion for a Single Rigid Body	p. 307
Introduction	p. 307
Configuration Manifold of an Unconstrained Rigid Body	p. 308
Lagrange's Equations of Motion: A First Form	p. 311
A Satellite Problem	p. 315
Lagrange's Equations of Motion: A Second Form	p. 318
Lagrange's Equations of Motion: Approach II	p. 324
Rolling Disks and Sliding Disks	p. 325
Lagrange and Poisson Tops	p. 331
Closing Comments	p. 336
Exercises	p. 336
Systems of Rigid Bodies	p. 345
Introduction to Multibody Systems	p. 347
Introduction	p. 347
Balance Laws and Lagrange's Equations of Motion	p. 347
Two Pin-Jointed Rigid Bodies	p. 349
A Single-Axis Rate Gyroscope	p. 351
Closing Comments	p. 355
Exercises	p. 355
Background on Tensors	p. 362
Introduction	p. 362
Preliminaries: Bases, Alternators, and Kronecker Deltas	p. 362
The Tensor Product of Two Vectors	p. 363
Second-Order Tensors	p. 364
A Representation Theorem for Second-Order Tensors	p. 364
Functions of Second-Order Tensors	p. 367
Third-Order Tensors	p. 370
Special Types of Second-Order Tensors	p. 372
Derivatives of Tensors	p. 373
Exercises	p. 374
Bibliography	p. 377
Index	p. 389
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