Classical Mechanics: A Modern Perspective

This book, although short, is a fairly good overview of classical mechanics, which emphasizes more recent developments in the theory, such as chaotic dynamical systems. The authors do however remain concrete in their treatment, with real-world examples permeating the text. The details behind the theory of classical mechanics are presented very quickly in the book, and this might make the book difficult to read for students first exposed to mechanics at this level. Chapter one is an introduction to motion in one dimension. After a brief review of Newton's laws, the authors solve some neat problems dealing with damping forces, one being the frictional force on a drag racer, and the other with aerodynamic drag on a parachute. They also treat the undamped and damped harmonic oscillator, and the discussion is very standard. The authors are careful to point out that some force laws are too complicated to be solved analytically, but that computing methods can be used to solve the cases that are not. Computational approaches are now the rule rather than the exception in problems in mechanics, and this trend will continue in the future. After a short discussion of energy conservation, the authors introduce motion in three dimensions and give a fairly detailed overview of vector notation. Their approach to tensors though is kind of antiquated, for it motivates them via the outer product, which is reminiscent of the dyadic approach that is currently "out of fashion". The authors also discuss the simple pendulum, but do not of course introduce the elliptic curve solutions that accompany this problem. Such a treatment, however fascinating, would drive this book to a height that would make it inaccessible to the audience of students it addresses. Coupled harmonic oscillators are solved using the normal mode approach. Lagrangian mechanics is introduced in chapter 3, but not from the standpoint of variational calculus at first. Instead the authors choose to present this formulation via generalized forces. They include a discussion of constraints, and give as an example the simple pendulum with a moving support. Only later do they give the Lagrangian formulation via variational calculus, and do so rather hurriedly. Hamilton's equations are derived, and it is shown (again briefly) how Legendre transformations enter into the formalism of Hamiltonian mechanics. Conservation principles are then thought of as fundamental in the rest of the book, and the authors use momentum conservation to discuss elastic and inelastic collisions in chapter 4. Angular momentum conservation is then used in chapter 5 to discuss central forces and planetary motion. Kepler's laws are also discussed, and Rutherford scattering is discussed. All of the discussion is pretty standard and can be found in most textbooks on classical mechanics. Rigid body mechanics makes its appearance in chapter 6, wherein the authors discuss the rotational equations of motion of many-particle systems and

Prof. Barger and Olsson show a new perspective in introducing the classical mechanics to junior level undergraduate in Physics. They successfully give a fresh treatment of mechanics by introducing the lagrangian in the earlier part of the book. Recommended for use in junior level mechanics physics.