Search results for "Conjugate and cut loci"

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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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Geometric and numerical techniques to compute conjugate and cut loci on Riemannian surfaces

2014

International audience; We combine geometric and numerical techniques - the Hampath code - to compute conjugate and cut loci on Riemannian surfaces using three test bed examples: ellipsoids of revolution, general ellipsoids, and metrics with singularities on S2 associated to spin dynamics.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Code (set theory)Spin dynamicsGeometryspin dynamics01 natural sciencesoptimal controlsymbols.namesakeGaussian curvature0101 mathematicsGeneral ellipsoidMathematics010102 general mathematics[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Optimal controlUmbilical pointEllipsoidOptimal controlCalcul parallèle distribué et partagé010101 applied mathematicsSpindynaicssymbolsgeneral ellipsoidGravitational singularity[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Conjugate and cut lociConjugate
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