JET BUNDLE GEOMETRY, DYNAMICAL CONNECTIONS, AND THE INVERSE PROBLEM OF LAGRANGIAN MECHANICS

Some aspects of the geometry of jet-bundles, especially relevant for t he formulation of Classical Mechanics, are investigated. The main resu lt is the construction of a tenser analysis on the first jet extension of the configuration space-time, based on a suitable linear connectio n, determined entirely by the dynamics of the system. The significance of this ''dynamical connection'' in the geometrization of Classical M echanics is discussed, paying a special attention to two particular as pects, namely the implementation of the concept of ''relative time der ivative'' in the Lagrangian framework, and the derivation of the Helmh oltz conditions for the inverse problem of Lagrangian Dynamics.