Journal of Lie Theory

no. 2
The Inverse Problem for Invariant Lagrangians on a Lie Group
Journal of Lie Theory, Volume 18 (2008) no. 2, pp. 471-502
We discuss the problem of the existence of a regular invariant Lagrangian for a given system of invariant second-order ordinary differential equations on a Lie group, using approaches based on the Helmholtz conditions. Although we deal with the problem directly on the tangent manifold of the Lie group, our main result relies on a reduction of the system on the tangent manifold to a system on the Lie algebra of the Lie group. We conclude with some illustrative examples.
DOI: 10.5802/jolt.506
Classification: 22E30, 49N45, 53C22, 53C60, 70H03
Keywords: Euler-Poincare equations, inverse problem, Lagrangian system, Lie group, reduction, second-order ordinary differential equations 
@article{JOLT_2008_18_2_a13,
     author = {M. Crampin and T. Mestdag},
     title = {The {Inverse} {Problem} for {Invariant} {Lagrangians} on a {Lie} {Group}},
     journal = {Journal of Lie Theory},
     pages = {471--502},
     year = {2008},
     volume = {18},
     number = {2},
     doi = {10.5802/jolt.506},
     zbl = {1148.22004},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.506/}
}
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M. Crampin; T. Mestdag. The Inverse Problem for Invariant Lagrangians on a Lie Group. Journal of Lie Theory, Volume 18 (2008) no. 2, pp. 471-502. doi: 10.5802/jolt.506

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