Analytical Mechanics
£64.99
- Author: Nivaldo A. Lemos, Universidade Federal Fluminense, Brazil
- Date Published: August 2018
- availability: In stock
- format: Hardback
- isbn: 9781108416580
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Analytical mechanics is the foundation of many areas of theoretical physics including quantum theory and statistical mechanics, and has wide-ranging applications in engineering and celestial mechanics. This introduction to the basic principles and methods of analytical mechanics covers Lagrangian and Hamiltonian dynamics, rigid bodies, small oscillations, canonical transformations and Hamilton–Jacobi theory. This fully up-to-date textbook includes detailed mathematical appendices and addresses a number of advanced topics, some of them of a geometric or topological character. These include Bertrand's theorem, proof that action is least, spontaneous symmetry breakdown, constrained Hamiltonian systems, non-integrability criteria, KAM theory, classical field theory, Lyapunov functions, geometric phases and Poisson manifolds. Providing worked examples, end-of-chapter problems, and discussion of ongoing research in the field, it is suitable for advanced undergraduate students and graduate students studying analytical mechanics.
Read more- Includes fully worked examples making the topic accessible and showing theory in practise
- Provides end-of-chapter problems to test understanding and enhance the reader's problem solving abilities
- Describes ongoing research and provides an extensive bibliography for further research
Reviews & endorsements
'The greatest strength of the book is that it starts with minimal knowledge and then takes the student very carefully into the modern concepts. The background required is a basic knowledge in classical dynamics and differential equations, with the other usual basic mathematics courses. By the end of the book the student is prepared for the advanced topics of modern geometric mechanics … I highly recommend this book as an advanced undergraduate text in mathematics, physics or engineering.' Thomas J. Bridges, Contemporary Physics
See more reviews'The contents cover the most relevant topics for an advanced undergraduate course on analytical mechanics, enlarged by a selection of topics of interest for graduate students and researchers. The chapter structure and subject sequence is carefully chosen, rendering a constructive and pedagogical approach.' Cesar Rodrigo, MathsSciNet
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×Product details
- Date Published: August 2018
- format: Hardback
- isbn: 9781108416580
- length: 470 pages
- dimensions: 254 x 192 x 25 mm
- weight: 0.18kg
- contains: 84 b/w illus.
- availability: In stock
Table of Contents
Preface
1. Lagrangian dynamics
2. Hamilton's variational principle
3. Kinematics of rotational motion
4. Dynamics of rigid bodies
5. Small oscillations
6. Relativistic mechanics
7. Hamiltonian dynamics
8. Canonical transformations
9. The Hamilton–Jacobi theory
10. Hamiltonian perturbation theory
11. Classical field theory
Appendix A. Indicial notation
Appendix B. Frobenius integrability condition
Appendix C. Homogeneous functions and Euler's theorem
Appendix D. Vector spaces and linear operators
Appendix E. Stability of dynamical systems
Appendix F. Exact differentials
Appendix G. Geometric phases
Appendix H. Poisson manifolds
Appendix I. Decay rate of fourier coefficients
References
Index.
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