Lectures in Nonlinear Mechanics and Chaos Theory

摘要

This concise book provides a rigorous introduction to the theory of nonlinear mechanics and chaos, suitable for students across physics, mathematics and engineering. Nonlinear dynamics treats problems that cannot be "solved", in the sense that it is not possible to derive equations of motion that describe the positions of the various parts of a system as functions of time using standard analytic functions. If, on one side, the formulations of mechanics of Lagrange and Hamilton lead to systems that cannot be solved in the usual sense of the word, perturbation theory, in turn, fails in providing approximate solutions because of the problem of small dividers. This is the path that led originally to the discovery of chaos, and it is the one that the author pursues in the book.