caa a22 4500 463196619 CHVBK 20180406164924.0 cr unu---uuuuu 170326e20071001xx s 000 0 eng 10.1007/s10773-007-9369-3 doi (NATIONALLICENCE)springer-10.1007/s10773-007-9369-3 Affine Hamiltonians in Higher Order Geometry [Elektronische Daten] [Paul Popescu, Marcela Popescu] Affine Hamiltonians are defined in the paper and their study is based especially on the fact that in the hyperregular case they are dual objects of Lagrangians defined on affine bundles, by mean of natural Legendre maps. The variational problems for affine Hamiltonians and Lagrangians of order k≥2 are studied, relating them to a Hamilton equation. An Ostrogradski type theorem is proved: the Hamilton equation of an affine Hamiltonian h is equivalent with Euler-Lagrange equation of its dual LagrangianL. Zermelo condition is also studied and some non-trivial examples are given. Springer Science+Business Media, LLC, 2007 Affine bundle nationallicence Higher order spaces nationallicence Lagrangian nationallicence Affine Hamiltonian nationallicence Vectorial Hamiltonian nationallicence Popescu Paul Department of Applied Mathematics, University of Craiova, 13, Al.I.Cuza st., 1100, Craiova, Romania aut Popescu Marcela Department of Applied Mathematics, University of Craiova, 13, Al.I.Cuza st., 1100, Craiova, Romania aut International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/10(2007-10-01), 2531-2549 0020-7748 46:10<2531 2007 46 10773 https://doi.org/10.1007/s10773-007-9369-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-007-9369-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Popescu Paul Department of Applied Mathematics, University of Craiova, 13, Al.I.Cuza st., 1100, Craiova, Romania aut NATIONALLICENCE 700 1- Popescu Marcela Department of Applied Mathematics, University of Craiova, 13, Al.I.Cuza st., 1100, Craiova, Romania aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/10(2007-10-01), 2531-2549 0020-7748 46:10<2531 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer