Lectures on Analytical Mechanics

Abstract

Abstract This book was written by working physicists for students and teachers of physics faculties of universities. It is based on the authors’ many years (140+ in total) of experience delivering lectures and seminars at the Faculty of Physics at Novosibirsk State University. The authors present analytical mechanics as the first part in the study of theoretical physics. Its methods and ideas are crucially important, as they form the basis of all other branches of theoretical physics, including quantum mechanics, statistical physics, and field theory. Such concepts as the Lagrangian and Hamiltonian formalisms, normal oscillations, adiabatic invariants, Liouville theorem, and canonical transformations lay the foundation, without which any further in-deep study of theoretical physics would be impossible. The book begins by discussing the motion of particles in a central field and scattering of particles based on Newton’s equations. It then introduces and explores the Lagrangian equations for various systems, linear and non-linear oscillations, the Hamiltonian formalism, and the motion of a rigid body. Each topic is accompanied by problems that are suitable for seminars and testing. This edition includes about ten new sections, which provide practical illustrations of the theoretical material. These sections can be used by teachers as a basis for conducting a specialized course, or by curious students who wish to explore different applications of analytical mechanics on their own.

Topics & Concepts