Geometric mechanics / Waldyr Muniz Oliva

The denomination "geometric mechanics'' is usually associated with the application of techniques and results from symplectic and Poisson geometry to mechanics, in particular to its Lagrangian and Hamiltonian formulations. The title of the present book, however, covers a somewhat different load: here geometric mechanics primarily refers to the treatment of Newtonian (non-relativistic) mechanics and relativistic mechanics on Riemannian and pseudo-Riemannian manifolds. The Lagrangian and Hamiltonian formulations of mechanics, and the basic aspects of symplectic geometry, are only indirectly touched upon. As such, this book, which is based on lecture notes of a graduate course taught by the author, clearly distinguishes itself, both in content and spirit, from most other textbooks dealing with a modern differential geometric approach to mechanics. ... (MathSciNet)