Structure and Interpretation of Classical Mechanics - Tapa dura

"Sussman and Wisdom have reinvented classical mechanics for the computer age, freeing their students from the unrealistic integrable systems that dominate the traditional course and leading them to realistic kinds of systems that can now be studied on modern computers. They do this with a passion for clarity and conceptual rigor that leads to new general insights as well. Soon we will all understand the Legendre transformation in their new and elegant way."--David Ritz Finkelstein, School of Physics, Georgia Institute of Technology "By making the physics precise enough to run on a computer, the authors open the door to a deeper understanding of classical reality, with the promise of a deeper understanding of all reality."--Piet Hut, Professor of Astrophysics, Institute for Advanced Study, Princeton, New Jersey "How can one write a new book on classical mechanics? Hasn't everything already been said? No! Things have changed. Now that there are computers, you can actually solve the equations of motion for interesting problems. Mathematical niceties are not the obsession of the authors, but rather to find out what happens, by a natural combination of mathematical argument and computer use. This new and effective approach should attract students to a subject which, since Newton, has constantly managed to rejuvenate itself."--David Ruelle, Honorary Professor, Institut des Hautes Etudes Scientifique, France

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 overlaps to help the student 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 student 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.