Abstract
A suitable “dual” for the k-acceleration bundle(T k M, πk,M) is the fiberedbundle (T k−1 M× M T*M). The mentioned bundle carries a canonicalpresymplectic structure and k canonical Poisson structures. By means of this“dual” we define the notion of Hamilton spaces of orderk, whose total spaceconsists of points x of the configuration spaceM, accelerations of order 1,...,k − 1, y (1),...,y (k−1), and momenta p. Some remarkable Hamiltonian systemsare pointed out. There exists a Legendre mapping from the Lagrange spaces oforder k to the Hamilton space of order k.
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Miron, R. Hamilton Spaces of Order k ≥ 1. International Journal of Theoretical Physics 39, 2327–2336 (2000). https://doi.org/10.1023/A:1003747816853
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DOI: https://doi.org/10.1023/A:1003747816853