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A 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...
| Call Number: | Libro Electrónico |
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| Main Authors: | , |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
Oxford :
Pergamon Press,
1966.
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| Edition: | First edition. |
| Series: | Pergamon international library of science, technology, engineering, and social studies.
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| Subjects: | |
| Online Access: | Texto completo |
Table of 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 o�i 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.