Analytical Mechanics
Analytical Mechanics
£68.00
GBPAnalytical 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.
- 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
'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
Product details
August 2018Hardback
9781108416580
470 pages
254 × 192 × 25 mm
0.18kg
84 b/w illus.
Available
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.
