Classical Mechanics by Richard A. Matzner

Classical mechanics has certainly changed in form since the days of Newton, due in part to the Lagrangian and Hamiltonian formulations, and to the rise of the theory of relativity. Student pursuing graduate study in mechanics will be exposed to differential geometry as well as other more abstract mathematics. Formulating mechanics using these mathematical tools has the advantage that it remains loyal to the spirit of the theory of relativity, especially the general theory, which makes heavy use of differential geometry. It has the disadvantage of not being amenable to numerical computation, and sometimes masks the underlying intuition. This short book proposes to be a "modern" introduction to classical mechanics, and it succeeds in its goal to a large degree. However, there is no discussion at all of chaos, in spite of its importance and modernity. Chaotic mechanical systems, although only discovered recently in comparison to the long history of mechanics, can still be thought of in the context of classical (Newtonian) mechanics, even though they are more easily formulated in the Hamiltonian formalism.