Geodesic
Connections over a~distribution and geodesic sprays
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2013), pp. 10-18

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We define (in a natural way) an almost contact metric structure on a smooth distribution of a contact metric manifold considered as the total space of a vector bundle. We introduce notions of a geodesic spray of a connection over a smooth distribution and of a generalized Hamiltonian system. In terms of this system we give an invariant description of the motion of a mechanical system with constraints.
Keywords: contact structure, Hamiltonian vector field, Reeb vector field, semispray, geodesic spray, symplectic structure. 
@article{IVM_2013_4_a1,
     author = {A. V. Bukusheva and S. V. Galaev},
     title = {Connections over a~distribution and geodesic sprays},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {10--18},
     publisher = {mathdoc},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_4_a1/}
}
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A. V. Bukusheva; S. V. Galaev. Connections over a~distribution and geodesic sprays. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2013), pp. 10-18. http://geodesic.mathdoc.fr/item/IVM_2013_4_a1/