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Group classification for path equation describing minimum drag work and symmetry reductions

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Abstract

The path equation describing the minimum drag work first proposed by Pakdemirli is reconsidered (Pakdemirli, M. 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 (5), 1113–1116 (2009)). The Lie group theory is applied to the general equation. The group classification with respect to an altitude-dependent arbitrary function is presented. Using the symmetries, the group-invariant solutions are determined, and the reduction of order is performed by the canonical coordinates.

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References

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Authors and Affiliations

  1. Department of Mechanical Engineering, Celal Bayar University, 45140, Muradiye Manisa, Turkey

    M. Pakdemirli & Y. Aksoy

Authors
  1. M. Pakdemirli
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  2. Y. Aksoy
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Corresponding author

Correspondence to M. Pakdemirli.

Additional information

Communicated by Xing-ming GUO

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Pakdemirli, M., Aksoy, Y. Group classification for path equation describing minimum drag work and symmetry reductions. Appl. Math. Mech.-Engl. Ed. 31, 911–916 (2010). https://doi.org/10.1007/s10483-010-1325-x

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  • DOI: https://doi.org/10.1007/s10483-010-1325-x

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Chinese Library Classification

2000 Mathematics Subject Classification

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