Screen LibraryA course of mathematics for engineers and scientists. Volume 6, Advanced theoretical mechanics /
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 me...
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| Published: |
Pergamon Press,
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| Publisher Address: | Oxford : |
| Publication Dates: | 1966. |
| Literature type: | eBook |
| Language: | English |
| Edition: | First edition. |
| Series: |
Pergamon international library of science, technology, engineering and social studies
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| Subjects: | |
| Online Access: |
http://www.sciencedirect.com/science/book/9780080250618 |
| Summary: |
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 analyt. |
| Item Description: | Includes index. |
| Carrier Form: | 1 online resource (518 pages) : illustrations. |
| ISBN: |
9781483137407 1483137406 |
| Index Number: | QA37 |
| CLC: | O1 |
| Contents: |
Front Cover; Advanced Theoretical Mechanics; Copyright Page; Table of Contents; PREFACE; CHAPTER 1. KINEMATICS IN THREE DIMENSIONS; 1:1 Introduction; 1:2 The transformation law for vectors; 1:3 Finite rotations; 1:4 Successive rotations: Euler's angles; 1:5 Angular velocity; 1:6 Relative motion; 1:7 Moving frames of reference; 1:8 The acceleration of a particle; 1:9 The general motion of a rigid body; 1:10 Angular velocities about non-intersecting axes; Miscellaneous Exercises I; CHAPTER 2. SETS OF FORCES: EQUILIBRIUM; 2:1 Introduction; 2:2 Equilibrium; 2:3 Equivalent sets of forces. 2:4 The principle of virtual work2:5 Other sets of line-vectors; Miscellaneous Exercises II; CHAPTER 3. THE DYNAMICS OF A PARTICLE; 3:1 General principles; 3:2 A particle with one degree of freedom; 3:3 The use of rotating and accelerated axes; 3:4 The spherical pendulum; 3:5 Motion on a surface of revolution; 3:6 Motion relative to the rotating earth; 3:7 The motion of a charged particle; Miscellaneous Exercises III; CHAPTER 4. THE MOTION OF A SYSTEM OF PARTICLES; 4:1 Description of the system; 4:2 The dynamical variables; 4:3 Conservation laws; 4:4 The inertia matrix. 4:5 Principal axes of inertia4:6 Dynamical variables for rigid systems; 4:7 The motion of a sphere; Miscellaneous Exercises IV; CHAPTER 5. GYROSCOPIC MOTION, FREE ROTATION AND STEADY MOTION; 5:1 Introduction; 5:2 Rotation under no forces oi bodies with kinetic symmetry; 5:3 The steady motion of a gyroscope or top; 5:4 The general motion of a top; 5:5 Euler's Dynamical Equations; 5:6 Free rotation; 5:7 More general motions; Miscellaneous Exercises V; CHAPTER 6. LAGRANGE'S EQUATIONS; 6:1 Generalised methods; 6:2 The dynamical variables; 6:3 Generalised forces; 6:4 Classification of constraints. 6:5 Application of the Principle of Virtual Work6:6 Conservation Laws; 6:7 Ignoration of coordinates; 6:8 The motion of a charged particle; Miscellaneous Exercises VI; CHAPTER 7. STABILITY OF MOTION; 7:1 Introduction; 7:2 Steady motion with two degrees of freedom; 7:3 The stability of free rotation of a rigid body; 7:4 The stability of a top; 7:5 The gyro-compass; 7:6 The stability of a rolling wheel; Miscellaneous Exercises VII; CHAPTER 8. IMPULSIVE MOTION; 8:1 Elementary discussion; 8:2 Generalised methods; 8:3 General theorems; Miscellaneous Exercises VIII. CHAPTER 9. THE OSCILLATIONS OF A DYNAMICAL SYSTEM WITH A FINITE NUMBER OF DEGREES OF FREEDOM -NORMAL MODES9:1 Introduction; 9:2 Systems with two degrees of freedom; 9:3 Stability of equilibrium: free oscillations of a system with n degrees of freedom; 9:4 The oscillations of a linearly constrained system-Rayleigh's principle; 9:5 A reciprocal theorem; Miscellaneous Exercises IX; CHAPTER 10. THE VIBRATIONS OF STRINGS; 10:1 The fundamental concepts of wave motion; 10:2 Transverse vibrations; 10:3 Normal modes; 10:4 Forced vibrations and damping. |