Nivaldo A. Lemos
Cambridge University Press; 2nd edition Revised
Analytical Mechanics, 2nd Edition (PDF), Revised is the foundation for many fields of theoretical physics, including statistical mechanics and quantum theory. It also has wide-ranging applications in engineering mechanics and celestial mechanics. The Hamiltonian and Lagrangian dynamics, tiny oscillations, rigid bodies, canonical transformations, and the Hamilton–Jacobi theory are all covered in this introduction to the fundamental principles and methods of analytical mechanics. This completely up-to-date PDF etextbook covers a variety of difficult topics, some of which have a topological or geometric flavor, and includes thorough mathematical appendices. These include constrained Hamiltonian systems, Bertrand's theorem, spontaneous symmetry breakdown, a demonstration that action is least, non-integrability requirements, KAM theory, Lyapunov functions, classical field theory, geometric phases, and Poisson manifolds. Other examples include: It is appropriate for graduate students as well as advanced undergraduate students who are studying analytical mechanics because it contains extensive worked examples, questions at the end of each chapter, and discussion of active research in the subject.
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