Group classification for path equation describing minimum drag work and symmetry reductions
The authors apply the symmetry group method to the path equation which describes the minimum drag work earlier proposed by the first author [``The drag work minimization path for a flying object with altitude-dependent drag parameters'', Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 223, No.~5, 1113--1116 (2009)]. They perform a Lie group classification with respect to the altitude dependent function. Various cases arise for which extensions of the principal Lie algebra are necessary. Cases which admit the maximal eight symmetries are significant. The symmetries obtained are used in two ways: (i) some group-invariant solutions are deduced and (ii) canonical coordinates are invoked to reduce the order of the equation. This contribution will appeal to those working in symmetries of ordinary differential equations and its applications.
scientific article; zbMATH DE number 5818460