By Kenneth Meyer, Glen Hall

This textual content grew out of graduate point classes in arithmetic, engineering and physics given at numerous universities. The classes took scholars who had a few heritage in differential equations and lead them via a scientific grounding within the concept of Hamiltonian mechanics from a dynamical structures standpoint. subject matters lined contain a close dialogue of linear Hamiltonian platforms, an advent to variational calculus and the Maslov index, the fundamentals of the symplectic crew, an advent to aid, functions of Poincaré's continuation to periodic recommendations, using common types, functions of mounted aspect theorems and KAM idea. there's a unique bankruptcy dedicated to discovering symmetric periodic suggestions by means of calculus of adaptations methods.

The major examples handled during this textual content are the N-body challenge and numerous really expert difficulties just like the limited three-body challenge. the idea of the N-body challenge is used to demonstrate the final thought. a few of the themes lined are the classical integrals and aid, imperative configurations, the life of periodic options by means of continuation and variational equipment, balance and instability of the Lagrange triangular point.

Ken Meyer is an emeritus professor on the collage of Cincinnati, Glen corridor is an affiliate professor at Boston collage, and Dan Offin is a professor at Queen's University.