Relative geodesics in the special Euclidean group

@article{Holm2013RelativeGI,
  title={Relative geodesics in the special Euclidean group},
  author={Darryl D. Holm and L. Noakes and J. Vankerschaver},
  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  year={2013},
  volume={469}
}
  • Darryl D. Holm, L. Noakes, J. Vankerschaver
  • Published 2013
  • Mathematics, Physics
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • We introduce a measurement (the discrepancy) of the minimum energy needed to transform from a standard parametrized planar curve c0 to an observed curve c1. To this end, we say that a curve of transformations in the special Euclidean group SE(2) is admissible if it maps the source curve to the target curve under the point-wise action of SE(2) on the plane. After endowing the group SE(2) with a left-invariant metric, we define a relative geodesic in SE(2) to be a critical point of the energy… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 26 REFERENCES
    Lie group methods
    107
    Continuous and Discrete Clebsch Variational Principles
    34
    Hamilton-Pontryagin Integrators on Lie Groups
    52
    Applications of lie groups to differential equations
    4712
    Discrete Hamilton-Pontryagin mechanics and generating functions on Lie groupoids
    9
    Discrete Geometric Optimal Control on Lie Groups
    73