0000000000302766

AUTHOR

Minoru Tanaka

showing 2 related works from this author

One-parameter family of Clairaut-Liouville metrics

2007

Riemannian metrics with singularities are considered on the $2$-sphere of revolution. The analysis of such singularities is motivated by examples stemming from mechanics and related to projections of higher dimensional (regular) sub-Riemannian distributions. An unfolding of the metrics in the form of an homotopy from the canonical metric on $\SS^2$ is defined which allows to analyze the singular case as a limit of standard Riemannian ones. A bifurcation of the conjugate locus for points on the singularity is finally exhibited.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]space mechanics49K15 53C20 70Q05$2$-sphere of revolution[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Mathematics::Differential Geometryunfolding
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Conjugate and cut loci of a two-sphere of revolution with application to optimal control

2008

Abstract The objective of this article is to present a sharp result to determine when the cut locus for a class of metrics on a two-sphere of revolution is reduced to a single branch. This work is motivated by optimal control problems in space and quantum dynamics and gives global optimal results in orbital transfer and for Lindblad equations in quantum control.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyWork (thermodynamics)Class (set theory)Quantum dynamicsCut locus02 engineering and technologySpace (mathematics)01 natural sciencesspace and quantum mechanicsoptimal control020901 industrial engineering & automationconjugate and cut loci0101 mathematics2-spheres of revolutionMathematical PhysicsMathematicsApplied Mathematics010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]53C20; 53C21; 49K15; 70Q05Optimal controlMetric (mathematics)[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Orbital maneuverAnalysis
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