From Euler's Determinism to Arnold's Chaos
This book can be used as a textbook for a graduate course on mechanics, or for self-study. There are problems that range from exercises that verify parts of the text, moderately difficult calculations, all the way up to suggested research projects. Connections to other disciplines of mathematics and physics are emphasized: quantum mechanics, optics, relativity, Riemannian geometry, metric geometry. Although this is not a book about computational physics, the ideas
that underlie modern numerical methods in mechanics are introduced as well. Several problems that can be solved using Mathematical or Sage (software) will improve the student's
understanding.Applied mathematicians, physicists and engineers will find the book entertaining and useful. Modern theories that are usually out of the reach of physics students (e.g., the KAM theorem) are introduced here. Ancient methods that are forgotten are brought back (Jacobi integral in the three body problem, Newton's iteration) and placed in a modern context.