Geodesic
Geodesics in the sub-Riemannian problem on the group $\mathrm{SO}(3)$
Sbornik. Mathematics, Tome 207 (2016) no. 7, pp. 915-941

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Geodesics of left-invariant sub-Riemannian structures are considered on the group $\mathrm{SO}(3)$. A complete description of periodic geodesics, their elementary properties, certain necessary conditions for minimality and estimates for the cut time and the diameter of the metric are presented. Bibliography: 32 titles.
Keywords: sub-Riemannian geometry, almost Riemannian geometry, optimal control, geodesic curves, cut time. 
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     author = {I. Yu. Beschastnyi and Yu. L. Sachkov},
     title = {Geodesics in the {sub-Riemannian} problem on the group $\mathrm{SO}(3)$},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_7_a1/}
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I. Yu. Beschastnyi; Yu. L. Sachkov. Geodesics in the sub-Riemannian problem on the group $\mathrm{SO}(3)$. Sbornik. Mathematics, Tome 207 (2016) no. 7, pp. 915-941. http://geodesic.mathdoc.fr/item/SM_2016_207_7_a1/