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Minimum L ∞ accelerations in Riemannian manifolds

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Abstract

Riemannian cubics are curves in Riemannian manifolds M that are critical points for the L 2 norm of covariant acceleration, and are already rather well studied as elementary curves for interpolation problems in engineering. In the present paper the L 2 norm is replaced by the L ∞ norm, which may be more appropriate for some applications. However it is more difficult to derive the analogue of the Euler-Lagrange equation for the L ∞ norm, requiring techniques from optimal control, and the resulting necessary conditions take a different form. These necessary conditions are examined when M is a sphere or a bi-invariant Lie group, and some examples are given.

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Authors and Affiliations

  1. School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia, 6009, Australia

    Lyle Noakes

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  1. Lyle Noakes
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Correspondence to Lyle Noakes.

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Communicated by: Helmut Pottmann

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Noakes, L. Minimum L ∞ accelerations in Riemannian manifolds. Adv Comput Math 40, 839–863 (2014). https://doi.org/10.1007/s10444-013-9329-9

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  • DOI: https://doi.org/10.1007/s10444-013-9329-9

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