Integrable Hamiltonian systems on complex Lie groups

DOI10.1090/memo/0838zbMath1085.53071OpenAlexW2077029061MaRDI QIDQ5713278

Velimir Jurdjevic

Publication date: 13 December 2005

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/memo/0838

zbMATH Keywords

optimal controlsymmetric spacesintegrabilityLie groupsHamiltonian systemselastic curvesco-adjoint orbitsorthonormal frame bundles

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Symmetries and conservation laws in mechanics of particles and systems (70S10) Geometry of classical groups (51N30)

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Unnamed Item ⋮ Optimal under-actuated kinematic motion planning on the \(\epsilon\)-group ⋮ Morse theory for elastica ⋮ Extendability of Kirchhoff elastic rods in complete Riemannian manifolds ⋮ Kirchhoff elastic rods in five-dimensional space forms whose centerlines are not helices ⋮ Integrable quadratic hamiltonians on the Euclidean group of motions ⋮ Lie algebras and integrable systems: elastic curves and rolling geodesics ⋮ Optimal geometric motion planning for a spin-stabilized spacecraft ⋮ Kirchhoff elastic rods in three-dimensional space forms ⋮ Kowalewski top and complex Lie algebras ⋮ Kirchhoff elastic rods in higher-dimensional space forms ⋮ Planning rigid body motions using elastic curves ⋮ The symplectic structure of curves in three dimensional spaces of constant curvature and the equations of mathematical physics ⋮ Rolling Problems on Spaces of Constant Curvature ⋮ Optimal control on Lie groups and integrable Hamiltonian systems ⋮ Superintegrability of left-invariant sub-Riemannian structures on unimodular three-dimensional Lie groups

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