Classical dynamics is one of the cornerstones of advanced education in physics and applied mathematics, with applications across engineering, chemistry and biology. In this book, the author uses a concise and pedagogical style to cover all the topics necessary for a graduate-level course in dynamics based on Hamiltonian methods. Readers are introduced to the impressive advances in the field during the second half of the twentieth century, including KAM theory and deterministic chaos. Essential to these developments are some exciting ideas from modern mathematics, which are introduced carefully and selectively. Core concepts and techniques are discussed, together with numerous concrete examples to illustrate key principles. A special feature of the book is the use of computer software to investigate complex dynamical systems, both analytically and numerically. This text is ideal for graduate students and advanced undergraduates who are already familiar with the Newtonian and Lagrangian treatments of classical mechanics. The book is well suited to a one-semester course, but is easily adapted to a more concentrated format of one-quarter or a trimester. A solutions manual and introduction to Mathematica (R) are available online at www.cambridge.org/Lowenstein.
John H. Lowenstein is Professor Emeritus of Physics at New York University and has been conducting research in nonlinear dynamics for more than 20 years. Prior to that, his research focus was in quantum field theory with an emphasis on soluble models and renormalized perturbation theory.
1. Fundamentals of classical dynamics; 2. Hamiltonian formalism; 3. Integrable systems; 4. Canonical perturbation theory; 5. Order and chaos in Hamiltonian systems; 6. The swing-spring; Appendix: Mathematica (R) samples; Index.