Engineering dynamics

Cover......Page 1
Overview\r......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 11
Acknowledgments......Page 15
1.1.1 Algebra and Computations......Page 17
1.1.2 Vector Calculus-Velocity and Acceleration......Page 25
1.2.1 Newton\'s Laws......Page 29
1.2.2 Systems of Units......Page 31
1.2.3 Energy and Momentum......Page 33
Galileo Galilei......Page 37
Leonhard Euler......Page 38
Joseph-Louis Lagrange......Page 39
Edward John Routh......Page 40
Walther Ritz......Page 41
SELECTED REFERENCES......Page 42
HOMEWORK PROBLEMS......Page 43
2.1 Path Variables......Page 46
2.1.1 Tangent and Normal Components......Page 47
2.1.2 Parametric Description of Curves......Page 54
2.1.3 Binormal Direction and Torsion of a Curve......Page 59
2.2 Rectangular Cartesian Coordinates......Page 61
2.3 Curvilinear Coordinates......Page 66
2.3.1 Cylindrical and Polar Coordinates......Page 67
2.3.2 Spherical Coordinates......Page 74
Coordinates and Unit Vectors......Page 80
Kinematical Formulas......Page 85
2.4 Mixed Kinematical Descriptions......Page 89
SELECTED REFERENCES......Page 97
HOMEWORK PROBLEMS......Page 98
3.1 Coordinate Transformations......Page 107
3.1.1 Rotation Transformations......Page 108
Simple Rotations......Page 115
Body-Fixed Rotations......Page 116
Space-Fixed Rotations......Page 119
Rotation About an Arbitrary Axis......Page 122
3.2 Displacement......Page 128
3.3 Time Derivatives......Page 135
3.4.1 Analytical Description......Page 143
3.4.2 Procedure......Page 144
3.5 Velocity and Acceleration Analysis Using a Moving Reference Frame......Page 150
3.6 Observations from a Moving Reference Frame......Page 163
SELECTED REFERENCES......Page 174
HOMEWORK PROBLEMS......Page 175
4.1 General Equations......Page 189
4.2 Eulerian Angles......Page 194
4.3 Interconnections and Linkages......Page 199
4.4 Rolling......Page 216
SELECTED REFERENCES......Page 231
HOMEWORK PROBLEMS......Page 232
5.1 Linear and Angular Momentum......Page 244
5.1.1 System of Particles......Page 245
5.1.2 Rigid Body-Basic Equations......Page 249
5.1.3 Kinetic Energy......Page 251
5.2 Inertia Properties......Page 256
5.2.1 Moments and Products of Inertia......Page 257
Parallel Axis Transformation......Page 269
Rotational Transformation......Page 274
5.2.3 Inertia Ellipsoid......Page 279
5.2.4 Principal Axes......Page 283
5.3 Rate of Change of Angular Momentum......Page 291
SELECTED REFERENCES......Page 301
HOMEWORK PROBLEMS......Page 302
6.1.1 Basic Considerations......Page 312
6.1.2 Procedural Steps......Page 316
6.2 Planar Motion......Page 335
6.3 Newton-Euler Equations for a System......Page 347
6.4.1 Impulse-Momentum Principles......Page 354
6.4.2 Work-Energy Principles......Page 359
6.4.3 Collisions of Rigid Bodies......Page 375
SELECTED REFERENCES......Page 389
HOMEWORK PROBLEMS......Page 390
7.1 Background......Page 407
7.1.1 Principle of Virtual Work......Page 408
7.1.2 Principle of Dynamic Virtual Work......Page 410
7.2 Generalized Coordinates and Kinematical Constraints......Page 412
7.2.1 Selection of Generalized Coordinates......Page 413
7.2.2 Constraint Equations......Page 416
7.2.3 Configuration Space......Page 424
7.3 Evaluation of Virtual Displacements......Page 430
7.3.1 Analytical Method......Page 431
7.3.2 Kinematical Method......Page 435
7.4.1 Definition of Generalized Forces......Page 442
7.4.2 Relation Between Constraint Forces and Conditions......Page 447
7.4.3 Conservative Forces......Page 460
7.5 Lagrange\'s Equations......Page 462
7.6 Solution of Equations for Holonomic Systems......Page 482
SELECTED REFERENCES......Page 491
HOMEWORK PROBLEMS......Page 492
8.1 Lagrange\'s Equations–Constrained Case......Page 508
8.2 Computational Methods......Page 524
8.2.1 Algorithms......Page 526
8.2.2 Numerical Error Checking......Page 536
8.2.3 Initial Conditions......Page 537
8.2.4 Analysis of Coulomb Friction......Page 552
SELECTED REFERENCES......Page 560
HOMEWORK PROBLEMS......Page 561
9.1 Hamilton\'s Principle......Page 568
9.1.1 Derivation......Page 569
9.1.2 Calculus of Variations......Page 574
9.1.3 Ritz Series Method......Page 581
9.2.1 Hamilton\'s Equations......Page 587
9.2.2 Conservation of the Hamiltonian......Page 594
9.2.3 Ignorable Coordinates and Routh\'s Method......Page 598
9.3 Formulations with Quasi-Coordinates......Page 604
9.3.1 Quasi-Velocities and Quasi-Coordinates......Page 605
9.3.2 Gibbs–Appell Equations......Page 610
9.3.3 Kane\'s Equations......Page 632
9.3.4 Relationship of the Formulations......Page 634
SELECTED REFERENCES......Page 642
HOMEWORK PROBLEMS......Page 644
10.1.1 Axisymmetric Bodies......Page 653
10.1.2 Arbitrary Bodies......Page 659
10.1.3 Poinsot\'s Construction for Arbitrary Bodies......Page 663
10.2 Spinning Top......Page 672
10.3.1 Free Gyroscope......Page 688
10.3.2 Gyrocompass......Page 693
10.3.3 Single-Axis Gyroscope......Page 701
SELECTED REFERENCES......Page 707
HOMEWORK PROBLEMS......Page 708
CENTROIDAL INERTIA PROPERTIES......Page 713
Answers to Selected Homework Problems......Page 719
Index......Page 735