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arXiv · 1712.02930

Sub-Riemannian cubics in SU(2)

Michael Swaddle·Lyle Noakes
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Abstract

Sub-Riemannian cubics are a generalisation of Riemannian cubics to a sub-Riemannian manifold. Cubics are curves which minimise the integral of the norm squared of the covariant acceleration. Sub-Riemannian cubics are cubics which are restricted to move in a horizontal subspace of the tangent space. When the sub-Riemannian manifold is also a Lie group, sub-Riemannian cubics correspond to what we call a sub-Riemannian Lie quadratic in the Lie algebra. The present article studies sub-Riemannian Lie quadratics in the case of $\mathfrak{su}(2)$, focusing on the long term dynamics.

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Michael Swaddle, Lyle Noakes. 2018-05-16. Sub-Riemannian cubics in SU(2). https://arxiv.org/abs/1712.02930

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