Bi-Jacobi fields and Riemannian cubics for left-invariant \(\mathrm{SO}(3)\)

DOI10.4310/CMS.2016.v14.n1.a3zbMath1330.70063WikidataQ115205105 ScholiaQ115205105MaRDI QIDQ900232

Tudor S. Ratiu, Lyle Noakes

Publication date: 21 December 2015

Published in: Communications in Mathematical Sciences (Search for Journal in Brave)

zbMATH Keywords

Riemannian manifoldLie groupJacobi fieldnonlinear optimal controlrigid bodymechanical systemtrajectory planningRiemannian cubic

Mathematics Subject Classification ID

Control problems involving ordinary differential equations (34H05) Robot dynamics and control of rigid bodies (70E60) Asymptotic expansions of solutions to ordinary differential equations (34E05) Motion of a rigid body in contact with a solid surface (70E18) Classical differential geometry (53A99) Variational principles of physics (49S05) Motion of a rigid body with a fixed point (70E17) Optimality conditions (49K99)

Related Items (3)

High-order splines on Riemannian manifolds ⋮ Riemannian cubics close to geodesics at the boundaries ⋮ Stochastic variational principles for dissipative equations with advected quantities

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