For easy reference, the author treats Lagrangian, Hamiltonian, and Newtonian mechanics separately – exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively.
This second, fully revised edition has been expanded to further emphasize the importance of the geometric approach. Starting from Hamilton′s principle, the author shows, from a geometric perspective, how "all" of classical physics can be subsumed within classical mechanics. Having developed the formalism in the context of classical mechanics, the subjects of electrodynamics, relativistic strings and general relativity are treated
as examples of classical mechanics. This modest unification of classical physics is intended to provide a background for the far more ambitious "grand unification" program of quantum field theory.
The final chapters develop approximate methods for the analysis of mechanical systems. Here the emphasis is more on practical perturbative methods than on the canonical transformation formalism. "Geometric Mechanics" features numerous illustrative examples and assumes only basic knowledge of Lagrangian mechanics.
2 Geometry of Mechanics, I, Linear
3 Geometry of Mechanics, II, Curvilinear
4 Geometry of Mechanics, III, Multilinear
5 Lagrange–Poincaré Description of Mechanics
6 Newtonian/Gauge Invariant Mechanics
7 Hamiltonian Treatment of Geometric Optics
8 Hamilton–Jacobi Theory
9 Relativistic Mechanics
10 Conservation Laws and Symmetry
11 Electromagnetic Theory
12 Relativistic Strings
13 General Relativity
14 Analytic Bases for Approximation
15 Linear Hamiltonian Systems
16 Perturbation Theory
17 Symplectic Mechanics