Dynamical systems: Approximate Lagrangians and Noether symmetries
2019 ◽
Vol 16
(10)
◽
pp. 1950160
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Keyword(s):
We determine the approximate Noether point symmetries of the variational principle characterizing second-order equations of motion of a particle in a (finite-dimensional) Riemannian manifold. In particular, the Lagrangian comprises of kinetic energy and a potential [Formula: see text], perturbed to [Formula: see text]. We establish a convenient system of approximate geometric conditions that suffices for the computation of approximate Noether symmetry vectors and moreover, simplifies the problem of the effect of higher orders of the perturbation. The general results are applied to several practical problems of interest and we find extra Noether symmetries at [Formula: see text].
Keyword(s):
2018 ◽
Vol 15
(11)
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pp. 1850191
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Keyword(s):
2019 ◽
Vol 16
(05)
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pp. 1950068
2007 ◽
Vol 5
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pp. 195-200
1989 ◽
Vol 03
(15)
◽
pp. 1185-1188
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2009 ◽
Vol 09
(02)
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pp. 205-215
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1990 ◽
Vol 112
(3)
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pp. 313-319
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