Structure And Interpretation Of Classical Mechanics - Sussman Gerald-Jay

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Résumé :
This textbook takes an innovative approach to the teaching of classical mechanics, emphasizing the development of general but practical intellectual tools to support the analysis of nonlinear Hamiltonian systems. The development is organized around a progressively more sophisticated analysis of particular natural systems and weaves examples throughout the presentation. Explorations of phenomena such as transitions to chaos, nonlinear resonances, and resonance overlap help the reader to develop appropriate analytic tools for understanding. Computational algorithms communicate methods used in the analysis of dynamical phenomena. Expressing the methods of mechanics in a computer language forces them to be unambiguous and computationally effective. Once formalized as a procedure, a mathematical idea also becomes a tool that can be used directly to compute results. The reader actively explores the motion of systems through computer simulation and experiment. This active exploration is extended to the mathematics. The requirement that the computer be able to interpret any expression provides strict and immediate feedback as to whether an expression is correctly formulated. The interaction with the computer uncovers and corrects many deficiencies in understanding.

Biographie:
Gerald Jay Sussman is Matsushita Professor of Electrical Engineering in the Department of Electrical Engineering and Computer Science, and jack Wisdom is Breene M. Kerr Professor of Planetary Science in the Department of Earth, Atmospheric, and Planetary Sciences, both at the Massachusetts Institute of Technology. Sussman is a coauthor of Structure and Interpretation of Computer Programs (MIT Press, second edition, 1996).

Sommaire:
["Lagrangian Mechanics","Rigid Bodies","Hamiltonian Mechanics","Phase Space Structure","Canonical Transformations","Canonical Perturbation Theory."]