2016
DOI: 10.1007/s10883-016-9337-4
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Cut Locus and Optimal Synthesis in Sub-Riemannian Problem on the Lie Group SH(2)

Abstract: Global optimality analysis in sub-Riemannian problem on the Lie group SH(2) is considered. We cutout open dense domains in the preimage and in the image of the exponential mapping based on the description of Maxwell strata. We then prove that the exponential mapping restricted to these domains is a diffeomorphism.Based on the proof of diffeomorphism, the cut time, i.e., time of loss of global optimality is computed on SH(2).We also consider the global structure of the exponential mapping and obtain an explicit… Show more

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Cited by 24 publications
(25 citation statements)
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“…The goal of this paper is, given a structure , to describe all SR quotient structures for two-dimensional ideals . These are exactly nilpotent SR structures with growth vector (2,3,5,6).…”
Section: Examplementioning
confidence: 99%
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“…The goal of this paper is, given a structure , to describe all SR quotient structures for two-dimensional ideals . These are exactly nilpotent SR structures with growth vector (2,3,5,6).…”
Section: Examplementioning
confidence: 99%
“…. Therefore, any quotient algebra by the two-dimensional ideal is a Carnot algebra with growth vector (2,3,5,6). Let us describe such algebras.…”
Section: Examplementioning
confidence: 99%
See 2 more Smart Citations
“…We hope that this is possible by (extension of) the symmetry method applied successfully for description of cut time in several sub-Riemannian and Riemannian problems [20][21][22][23][24]. This question will be studied in forthcoming papers.…”
mentioning
confidence: 99%