Autonomous three dimensional Newtonian systems which admit Lie and Noether point symmetries

Details Autonomous three dimensional Newtonian systems which admit Lie and Noether point symmetries Autonomous three dimensional Newtonian systems which admit Lie and Noether point symmetries

2011-11-03

arxiv.org/abs/1111.0810v2

Physics

Classical Physics

12 pages

Scientific paper

We determine the autonomous three dimensional Newtonian systems which admit Lie point symmetries and the three dimensional autonomous Newtonian Hamiltonian systems, which admit Noether point symmetries. We apply the results in order to determine the two dimensional Hamiltonian dynamical systems which move in a space of constant non-vanishing curvature and are integrable via Noether symmetries. The derivation of the results is geometric and can be extended naturally to higher dimensions.

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