Nivaldo A. LemosCambridge University PressEdition: 2nd Revised ed., 8/9/2018EAN 9781108416580, ISBN10: 1108416586Hardcover, 470 pages, 25.4 x 19.2 x 2.5 cmLanguage: EnglishAnalytical 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.Preface1. Lagrangian dynamics2. Hamilton's variational principle3. Kinematics of rotational motion4. Dynamics of rigid bodies5. Small oscillations6. Relativistic mechanics7. Hamiltonian dynamics8. Canonical transformations9. The Hamilton–Jacobi theory10. Hamiltonian perturbation theory11. Classical field theoryAppendix A. Indicial notationAppendix B. Frobenius integrability conditionAppendix C. Homogeneous functions and Euler's theoremAppendix D. Vector spaces and linear operatorsAppendix E. Stability of dynamical systemsAppendix F. Exact differentialsAppendix G. Geometric phasesAppendix H. Poisson manifoldsAppendix I. Decay rate of fourier coefficientsReferencesIndex.
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