GEOMETRIC STUDY OF HAMILTON'S VARIATIONAL PRINCIPLE

Higher order tangent bundle geometry and sections along maps are used in Geometrical Mechanics in order to develop an intrinsic variational calculus. The role of variational derivative as the bundle operator associated to exterior differential on the set of trajectories is remarked. Euler-Lagrange equations and Poincaré-Cartan form are rederived in this way. Helmholtz conditions for the inverse problem of Lagrangian Mechanics are geometrically obtained for the general higher order case.