Higher-order Noether symmetries and constants of the motion
- 1 February 1981
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 14 (2) , 479-492
- https://doi.org/10.1088/0305-4470/14/2/023
Abstract
The authors identify a class of symmetries for Lagrangian systems, called higher-order Noether symmetries, which yield a corresponding first integral without further integrations. First, a version of Noether's theorem is recalled in which Noether symmetries are considered to be symmetries of the two-form d theta , theta being the Cartan form. nth-order Noether symmetries are then defined by the requirement LYnd theta =0. The picture is further generalised by exploring various ways in which the computation of repeated Lie derivatives of d theta can lead to the identification of first integrals. A number of illustrative examples are discussed.Keywords
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