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Mechanical Structures on Lie Algebroids

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Abstract

In this paper, we extend the study of mechanical systems in the general framework of Lie algebroids using the associated evolution nonlinear connections. In the case of the prolongations of a Lie algebroid over the vector bundle projections, we prove the equivalence between a regular section and a mechanical structure. Finally, we justify this construction with an example from optimal control theory.

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Acknowledgements

The author wishes to express his thanks to the referees for useful comments and suggestions concerning this paper.

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Authors and Affiliations

  1. Department of Statistics and Economic Informatics, University of Craiova, 13, Al. I. Cuza St., 200585, Craiova, Romania

    Liviu Popescu

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  1. Liviu Popescu
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Correspondence to Liviu Popescu.

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Popescu, L. Mechanical Structures on Lie Algebroids. Mediterr. J. Math. 15, 154 (2018). https://doi.org/10.1007/s00009-018-1204-y

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  • DOI: https://doi.org/10.1007/s00009-018-1204-y

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