Advanced dynamics

S. Ying9781563472244, 1-56347-224-4

Advanced Dynamics is recognized as an important subject of study for all engineering students and professionals in competitive university programs and throughout the industry. This textbook adeptly explains the fundamental laws of motion, but goes a step beyond by covering new topics such as gyroscopic effects, missile trajectories, interplanetary missions, multistage rockets, and use of numerical methods. In addition, theories such as the rotation operator are taken to a new degree and developed further, far surpassing comparable textbooks.
The book balances theory and application and relates all subjects to practical problems, real-world situations, and recent advances that affect everyday life. This text distinguishes itself with a more complete introduction to recent developments in dynamics, new and practical applications to help the reader remember key theories and uses, and an appreciation that the subject matter is riddled with ongoing problems that need new solutions. These distinguishing features make Advanced Dynamics more complete, interesting, and understandable than existing textbooks and resource materials. Problems appear at the end of each chapter, and a complimentary solutions manual is available for professors.
Advanced Dynamics is also written for those engineers who want to update their knowledge and stay current of the changes in the field, but do not have the opportunity to attend formal classes. The reader will take away a thorough understanding of the foundation of mechanical engineering, which is necessary to read and assimilate scholarly papers and leading articles published in journals and peer-reviewed magazines.

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Table of contents :
Front Matter……Page 1
Foreword……Page 3
Preface……Page 4
Table of Contents……Page 0
Table of Contents……Page 7
1.1 Dimensions and Units……Page 10
1.2 Elements and Vector Analysis……Page 11
1.3 Statics and Dynamics……Page 14
1.5 D’Alembert’s Principle……Page 15
1.6 Virtual Work……Page 16
Problems……Page 19
2.1 Kinematics of a Particle……Page 22
2.2 Particle Kinetics……Page 25
2.3 Angular Momentum (Moment of Momentum) of a Particle……Page 28
2.5 Conservative Forces……Page 30
Problems……Page 32
3.1 Conversion of Coordinates……Page 35
3.2 Collision of Particles in Midair……Page 39
3.3 General Motion of a System of Particles……Page 45
3.4 Gravitational Force and Potential Energy……Page 48
3.5 Collision of Two Spheres on a Plane……Page 52
Problems……Page 58
4.1 Generalized Coordinates, Velocities, and Forces……Page 61
4.2 Lagrangian Equations……Page 63
4.3 Hamilton’s Principle……Page 74
4.4 Lagrangian Equations with Constraints……Page 78
4.5 Calculus of Variations……Page 84
Problems……Page 91
5.1 Single-Stage Rockets……Page 93
5.2 Multistage Rockets……Page 98
5.3 Motion of a Particle in Central Force Field……Page 100
5.4 Space Vehicle with Electrical Propulsion (equations solved by small perturbation method)……Page 111
5.5 Interplanetary Trajectories……Page 115
Problems……Page 120
6.1 Linear Transformation Matrices……Page 122
6.2 Application of Linear Transformation to Rotation Matrix……Page 126
6.3 Cartesian Tensors and Dyadics……Page 128
6.4 Tensor of Inertia……Page 133
6.5 Principal Stresses and Axes in a Three-Dimensional Solid……Page 136
6.6 Viscous Stress in Newtonian Fluid……Page 140
6.7 Rotation Operators……Page 143
Problems……Page 154
7. Dynamics of a Rigid Body……Page 157
7.2 Relationship Between Derivatives of a Vector for Different Reference Frames……Page 158
7.3 Euler’s Angular Velocity and Equations of Motion……Page 162
7.4 Gyroscopic Motion……Page 168
7.5 Motion of a Heavy Symmetrical Top……Page 174
7.6 Torque on a Satellite in Circular Orbit……Page 178
Problems……Page 183
8. Fundamentals of Small Oscillations……Page 186
8.1 Fourier Series and Fourier Integral……Page 187
8.2 Fourier and Laplace Transforms……Page 200
8.3 Properties of Laplace Transforms……Page 202
8.4 Forced Harmonic Vibration Systems with Single Degree of Freedom……Page 208
8.5 Transient Vibration……Page 219
8.6 Response Spectrum……Page 226
8.7 Applications of Fourier Transforms……Page 229
Problems……Page 233
9. Vibration of Systems with Multiple Degrees of Freedom……Page 237
9.1 Vibration Systems with Two Degrees of Freedom……Page 238
9.2 Matrix Formulation for Systems with Multiple Degrees of Freedom……Page 248
9.3 Lumped Parameter Systems with Transfer Matrices……Page 259
9.4 Vibrations of Continuous Systems……Page 270
9.5 Nonlinear Vibrations……Page 293
9.6 Stability of Vibrating Systems……Page 298
Problems……Page 303
10. Special Relativity Theory……Page 308
10.1 Lorentz Transformation……Page 309
10.2 Brehme Diagram……Page 313
10.3 Immediate Consequences in Kinematics and Dynamics……Page 317
Problems……Page 320
Appendix A: Runge-Kutta Method……Page 322
Appendix B: Stoke’s Theorem……Page 324
Appendix C: Planetary Data……Page 327
Appendix D: Determinants and Matrices……Page 328
Appendix E: Method of Partial Fractions……Page 332
Appendix F: Tables of Fourier and Laplace Transforms……Page 336
Appendix G: Contour Integration and Inverse Laplace Transform……Page 339
Appendix H: Bessel Functions……Page 349
Appendix I: Instructions for Computer Programs……Page 363
Appendix J: Further Reading……Page 364
F……Page 365
P……Page 366
V……Page 367
W……Page 368