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Noether symmetries and integrability in time-dependent Hamiltonian mechanics
Theoretical and applied mechanics, Tome 43 (2016) no. 2, p. 255 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincaré--Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincaré--Cartan form is contact, the explicit expression for the symmetries in the inverse Noether theorem is given. As examples, we consider natural mechanical systems, in particular the Kepler problem. Finally, we prove a variant of the theorem on complete (non-commutative) integrability in terms of Noether symmetries of time-dependent Hamiltonian systems.
DOI : 10.2298/TAM160121009J
Classification : 37J15, 37J35, 37J55, 70H25, 70H33
Keywords: symmetries, the principle of stationary action, Poincaré--Cartan form, contact Hamiltonin vector fields, Noether theorem 
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     author = {Bo\v{z}idar Jovanovi\'c},
     title = {Noether symmetries and integrability in time-dependent {Hamiltonian} mechanics},
     journal = {Theoretical and applied mechanics},
     pages = {255 },
     year = {2016},
     volume = {43},
     number = {2},
     doi = {10.2298/TAM160121009J},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/TAM160121009J/}
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Božidar Jovanović. Noether symmetries and integrability in time-dependent Hamiltonian mechanics. Theoretical and applied mechanics, Tome 43 (2016) no. 2, p. 255 . doi: 10.2298/TAM160121009J

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