Abstract
The transformation properties of determined, autonomous systems of second-order ordinary differential equations, identified as vector fields on the tangent bundle of the space of dependent variables, are derived and studied. The inverse problem of Lagrangian dynamics is studied from this transformation viewpoint as well as the problem of alternative Lagrangians. In particular, regular Lagrangians which are analytic as functions of the first derivatives are considered. Finally, the inverse problem for second-order systems corresponding to the geodesic flow of a symmetric linear connection is investigated.
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