Affiliation:
1. School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa
Abstract
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].
Funder
National Research Foundation of South Africa
Publisher
World Scientific Pub Co Pte Lt
Subject
Physics and Astronomy (miscellaneous)
Cited by
7 articles.
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