The study of higher-order mechanics, by various geometrical methods, in the framework of the theory of higher-order tangent bundles or jet spaces, has been undertaken by a number of authors recently: for example, Tulczyjew [16, 17], Rodrigues [14, 15] de León [8], Krupka and Musilova [11, and references therein]. In this article we wish to complement these studies by approaching the subject from a new point of view, one which we developed for second-order differential equation fields and first-order Lagrangian mechanics in [19]. In particular, our aim is to show that many of the results we obtained there may be extended to the higher-order case.
Higher order tangent bundles of projective spaces and lens spaces