Mathematics and Mechanics - The Interplay : Volume II: Dynamical Systems

This book is to present a highly readable introduction to dynamical systems, namely initial-value problems of systems of differential equations (mathematics), and particle dynamics (mechanics).

This book is to present a highly readable introduction to dynamical systems, namely initial-value problems of systems of differential equations (mathematics), and particle dynamics (mechanics). Linear algebra is extensively covered as a prerequisite. This is the stand-alone second volume of a book that covers an integrated approach to mathematics and mechanics from elementary to graduate level material of scientific curricula-the first of this breadth. A simple, intuitive approach is used throughout. In particular, gut-level proofs are preferred over abstract ones, even if not succinct and elegant. To make the volume simple to read and, at the same time, rigorous, additional material (clearly marked as optional) is provided. Overall, every statement is proven-the sentence “it may be shown that . . . ” is banned from this book. Continuum systems, such as strings, pipes, membranes, and beams, are briefly addressed as limiting cases of discrete ones, with applications to musical string-and wind-instruments. Advanced material includes: Jordan matrices, power spectral density with application to clean-air-turbulence response, and approximate solutions of nonlinear differential equations by multiple scales and normal form, with application to limit cycles and post-flutter analysis. For completeness, there is an introduction to the numerical integration of differential equations and other computational techniques, in particular optimization and its relationship with genetic algorithms, neural networks, and artificial intelligence.