NEW ASPECTS ON THE GEOMETRY AND DYNAMICS OF QUADRATIC HAMILTONIAN SYSTEMS ON (𝔰𝔬(3))*

DOI10.1142/S0219887811005889zbMath1326.70027MaRDI QIDQ2891191

Răzvan M. Tudoran, Anania Gîrban, Cora Dăniasă

Publication date: 13 June 2012

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

zbMATH Keywords

periodic orbitsintegrabilityheteroclinic orbitsstability theoryWhitney stratificationsenergy-Casimir mappingPoisson dynamics

Mathematics Subject Classification ID

Hamilton's equations (70H05) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics (70K44) Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14)

Related Items (6)

Asymptotic stabilization with phase of periodic orbits of three-dimensional Hamiltonian systems ⋮ On the control of stability of periodic orbits of completely integrable systems ⋮ Invariant Control Systems on Lie Groups ⋮ Quadratic Hamilton-Poisson systems on \(\mathfrak{se}(1,1)^{*}_{-}\): the inhomogeneous case ⋮ Quadratic Hamilton-Poisson systems in three dimensions: equivalence, stability, and integration ⋮ Quadratic Hamilton–Poisson systems on $\mathfrak{s}\mathfrak{e}(1, 1)^{*}_{-}$: The homogeneous case

Cites Work

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• Classical and quantum dynamics for an extended free rigid body
• Integrable Euler equations on SO(4) and their physical applications
• Euler equations on finite dimensional Lie algebras arising in physical problems
• Normal modes for nonlinear Hamiltonian systems
• Nonlinear stability of fluid and plasma equilibria
• QUADRATIC AND HOMOGENEOUS HAMILTON–POISSON SYSTEM ON (so(3))
• Matrix Analysis
• Lectures on Mechanics
• Analytic and geometric study of stratified spaces

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