Geometric Mechanics - Toward a Unification of Classical Physics 2e (Hardcover, 2nd, Revised And Enlarged Edition)

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.

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