Analytical Mechanics and Integrable Systems
Analytical mechanics is the basic tool we will utilize through the whole book. The aim of this chapter is to succinctly introduce and define some basic concepts, such as Hamilton equations, symplectic (i.e., canonical) transformations, symmetry and reduction, integrable systems, and action-angle variables. This will be done in the third section of the chapter. In the first two sections we recall the main ideas of differential geometry and Lie groups, which are the natural language of analytical mechanics.
KeywordsAnalytical Mechanics Poisson Bracket Symplectic Manifold Poisson Structure Symplectic Structure
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