Chirgwin / Plumpton Advanced Theoretical Mechanics

A Course of Mathematics for Engineers and Scientists
1. Auflage 2013
ISBN: 978-1-4831-3740-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 518 Seiten, Web PDF

Advanced Theoretical Mechanics deals with advanced theoretical mechanics in three dimensions, making use of concepts and methods such as matrices, vectors, tensors, and transformation methods. The definition of a vector via the transformation law obeyed by its components is emphasized, and matrix methods are used to handle sets of components. Special attention is given to the definition of angular velocity and the proof that it can be represented by a vector. This book is comprised of 11 chapters and begins with an introduction to kinematics in three dimensions. Lagrange's equations and analytical dynamics are then presented, along with the simpler problems of three-dimensional dynamics, often with the help of rotating axes. Stability and small oscillations are also considered. The subsequent chapters focus on the dynamics of a particle and the motion of a system of particles; gyroscopic motion, free rotation, and steady motion; oscillations of a dynamical system with a finite number of degrees of freedom; and the vibrations of strings. The final chapter is devoted to analytical dynamics, paying particular attention to Hamilton's principle and equations of motion as well as the Hamilton-Jacobi equation. This monograph is intended for engineers and scientists as well as students of mathematics, physics, and engineering.

Autoren/Hrsg.

Chirgwin, Brian H.

Plumpton, Charles

Inhaltsverzeichnis

1;Front Cover;1
2;Advanced Theoretical Mechanics;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE;8
6;CHAPTER 1. KINEMATICS IN THREE DIMENSIONS;10
6.1;1:1 Introduction;10
6.2;1:2 The transformation law for vectors;11
6.3;1:3 Finite rotations;13
6.4;1:4 Successive rotations: Euler's angles;21
6.5;1:5 Angular velocity;27
6.6;1:6 Relative motion;35
6.7;1:7 Moving frames of reference;37
6.8;1:8 The acceleration of a particle;38
6.9;1:9 The general motion of a rigid body;45
6.10;1:10 Angular velocities about non-intersecting axes;50
6.11;Miscellaneous Exercises I;54
7;CHAPTER 2. SETS OF FORCES: EQUILIBRIUM;57
7.1;2:1 Introduction;57
7.2;2:2 Equilibrium;57
7.3;2:3 Equivalent sets of forces;65
7.4;2:4 The principle of virtual work;76
7.5;2:5 Other sets of line-vectors;87
7.6;Miscellaneous Exercises II;88
8;CHAPTER 3. THE DYNAMICS OF A PARTICLE;91
8.1;3:1 General principles;91
8.2;3:2 A particle with one degree of freedom;93
8.3;3:3 The use of rotating and accelerated axes;95
8.4;3:4 The spherical pendulum;104
8.5;3:5 Motion on a surface of revolution;113
8.6;3:6 Motion relative to the rotating earth;119
8.7;3:7 The motion of a charged particle;127
8.8;Miscellaneous Exercises III;134
9;CHAPTER 4. THE MOTION OF A SYSTEM OF PARTICLES;138
9.1;4:1 Description of the system;138
9.2;4:2 The dynamical variables;140
9.3;4:3 Conservation laws;143
9.4;4:4 The inertia matrix;145
9.5;4:5 Principal axes of inertia;148
9.6;4:6 Dynamical variables for rigid systems;157
9.7;4:7 The motion of a sphere;169
9.8;Miscellaneous Exercises IV;183
10;CHAPTER 5. GYROSCOPIC MOTION, FREE ROTATION AND STEADY MOTION;186
10.1;5:1 Introduction;186
10.2;5:2 Rotation under no forces oî bodies with kinetic symmetry;187
10.3;5:3 The steady motion of a gyroscope or top;193
10.4;5:4 The general motion of a top;200
10.5;5:5 Euler's Dynamical Equations;216
10.6;5:6 Free rotation;218
10.7;5:7 More general motions;231
10.8;Miscellaneous Exercises V;237
11;CHAPTER 6. LAGRANGE'S EQUATIONS;241
11.1;6:1 Generalised methods;241
11.2;6:2 The dynamical variables;242
11.3;6:3 Generalised forces;246
11.4;6:4 Classification of constraints;249
11.5;6:5 Application of the Principle of Virtual Work;251
11.6;6:6 Conservation Laws;268
11.7;6:7 Ignoration of coordinates;279
11.8;6:8 The motion of a charged particle;283
11.9;Miscellaneous Exercises VI;286
12;CHAPTER 7. STABILITY OF MOTION;290
12.1;7:1 Introduction;290
12.2;7:2 Steady motion with two degrees of freedom;291
12.3;7:3 The stability of free rotation of a rigid body;295
12.4;7:4 The stability of a top;297
12.5;7:5 The gyro-compass;301
12.6;7:6 The stability of a rolling wheel;306
12.7;Miscellaneous Exercises VII;313
13;CHAPTER 8. IMPULSIVE MOTION;315
13.1;8:1 Elementary discussion;315
13.2;8:2 Generalised methods;327
13.3;8:3 General theorems;338
13.4;Miscellaneous Exercises VIII;353
14;CHAPTER 9. THE OSCILLATIONS OF A DYNAMICAL SYSTEM WITH A FINITE NUMBER OF DEGREES OF FREEDOM —NORMAL MODES;356
14.1;9:1 Introduction;356
14.2;9:2 Systems with two degrees of freedom;359
14.3;9:3 Stability of equilibrium: free oscillations of a system with n degrees of freedom;369
14.4;9:4 The oscillations of a linearly constrained system—Rayleigh's principle;385
14.5;9:5 A reciprocal theorem;389
14.6;Miscellaneous Exercises IX;391
15;CHAPTER 10. THE VIBRATIONS OF STRINGS;395
15.1;10:1 The fundamental concepts of wave motion;395
15.2;10:2 Transverse vibrations;401
15.3;10:3 Normal modes;414
15.4;10:4 Forced vibrations and damping;427
15.5;10:5 Reflection and transmission at a discontinuity;432
15.6;10:6 Longitudinal vibrations;440
15.7;10:7 Application of Rayleigh's principle;446
15.8;10:8 Miscellaneous problems;449
15.9;Miscellaneous Exercises X;460
16;CHAPTER 11. ANALYTICAL DYNAMICS;465
16.1;11:1 Introduction;465
16.2;11:2 Hamilton's principle;465
16.3;11:3 The principle of least action;472
16.4;11:4 Hamilton's equations of motion;477
16.5;11:5 Transformation theory: contact transformations;486
16.6;11:6 Infinitesimal contact transformations;493
16.7;11:7 The Hamilton–Jacobi equation;496
16.8;Miscellaneous Exercises XI;503
17;ANSWERS TO THE EXERCISES;506
18;INDEX;516