Nivaldo A. Lemos

Analytical Mechanics (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 9. August 2018
• Englisch
• ISBN-13: 9781108265942
• Artikelnr.: 54081171

Autorenporträt

Nivaldo A. Lemos is Associate Professor of Physics at Universidade Federal Fluminense, Brazil. He was previously a visiting scholar at the Massachusetts Institute of Technology. His main research areas are quantum cosmology, quantum field theory and the teaching of classical mechanics.

Inhaltsangabe

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.