附註:Includes bibliographical references (pages 427-436) and index.
Cover -- Contents -- Preface -- Introduction -- I Analytical Mechanics -- 1 The Lagrangian Coordinates -- 1.1 A Primer for Various Formulations of Dynamics -- 1.2 Constraints -- 1.3 Degrees of Freedom and Lagrangian Coordinates -- 1.4 The Calculus of Variations and the Lagrange Equations -- 1.5 Remarks on Lagrange's Equations -- 2 Hamiltonian Systems -- 2.1 The Legendre Transformation -- 2.2 The Hamilton Equations -- 2.3 The Poisson Bracket and the Jacobi-Poisson Theorem -- 2.4 A More Compact Form of The Hamiltonian Dynamics -- 2.5 The Variational Principle for the Hamilton Equations -- 3 Transformation Theory -- 3.1 Canonical, Completely Canonical and Symplectic Transformations -- 3.2 A New Characterization of Completely Canonical Transformations -- 3.3 New Characterization of Sympletic Transformations -- 4 The Integration Methods -- 4.1 Integrals Invariants of a Differential System -- 4.2 A Primer on the Lie Derivative -- 4.3 The Kepler Dynamics.
摘要:This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a m.
