Analytical Mechanics

An introduction to the basic principles and methods of analytical mechanics, with selected examples of advanced topics and areas of ongoing research.

Nivaldo A. Lemos (Author)

9781108416580, Cambridge University Press

Hardback, published 9 August 2018

470 pages, 84 b/w illus.
25.4 x 19.2 x 2.5 cm, 0.18 kg

'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

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.

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.

Subject Areas: Classical mechanics [PHD], Physics [PH]