Lie algebras and integrable systems: elastic curves and rolling geodesics

DOI10.1134/s0081543823020098zbMath1527.37065OpenAlexW4386702471MaRDI QIDQ6072977

Velimir Jurdjevic

Publication date: 15 September 2023

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543823020098

zbMATH Keywords

Lie algebraHamiltonian systemsRiemannian manifoldsisospectral curves

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Applications of Lie algebras and superalgebras to integrable systems (17B80) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Differential geometric aspects in kinematics (53A17) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37)

Cites Work

• Integrable Hamiltonian systems connected with graded Lie algebras
• The geometry of the plate-ball problem
• Rigidity of integral curves of rank 2 distributions
• Control theory from the geometric viewpoint.
• Kowalewski top and complex Lie algebras
• Symmetric spaces rolling on flat spaces
• Optimal Control and Geometry: Integrable Systems
• Rolling sphere problems on spaces of constant curvature
• Non-Euclidean Elastica
• The rolling problem: overview and challenges
• Integrable Hamiltonian systems on complex Lie groups
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