Global methods in classical mechanics. The Euler-Lagrange equation (Q1272672)

First, the author reviews some basic definitions concerning smooth manifolds and mappings, tangent and cotangent bundles, action integrals on the tangent bundle, etc. Then the Euler-Lagrange system is derived as the main result of the application of concepts of admissible variations, Poincaré-Cartan 2-form, and Euler-Lagrange morphism. In the reviewer's opinion, introductory definitions of charts and of action seem to be not quite correct; additionally, many advanced topics are not explained.