Affinely rigid body and Hamiltonian systems on GL(n,\({\mathbb{R}})\)

DOI10.1016/0034-4877(88)90006-7zbMath0679.70010OpenAlexW2027514541MaRDI QIDQ1823042

Jan Jerzy Sławianowski

Publication date: 1988

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0034-4877(88)90006-7

zbMATH Keywords

Hamiltonian systemsaffine grouppseudo-Riemannian structuresdoubly- isotropic modelsdoubly-isotropic dynamicshyperbolic-Sutherland lattices

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Dynamics of a rigid body and of multibody systems (70E99) Axiomatics, foundations (70A05)

Related Items

Affine models of internal degrees of freedom and their action-angle description. ⋮ Linear frames in manifolds, Riemannian structures and description of internal degrees of freedom. ⋮ Invariant geodetic problems on the affine group and related Hamiltonian systems. ⋮ Some aspects of affine motion and nonholonomic constraints. Two ways to describe homogeneously deformable bodies ⋮ Persistence of Hamiltonian relative periodic orbits. ⋮ Constraints and symmetry in mechanics of affine motion ⋮ Quantization of affinely rigid body in \(n\)-dimensions ⋮ Motion of test rigid bodies in Riemannian spaces. ⋮ Affine symmetry in mechanics of collective and internal modes. I: Classical models ⋮ Quantum systems on linear groups ⋮ Dynamics of affinely deformable bodies from the standpoint of theoretical mechanics and differential geometry ⋮ Stability of relative equilibria. I: The reduced energy-momentum method ⋮ Models of internal degrees of freedom based on classical groups and their homogeneous spaces.

Cites Work

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• The moment map and collective motion
• Theory of nonlinear lattices
• The mechanics of an affinely-rigid body
• Deformable gyroscope in a non-Euclidean space classical, nonrelativistic theory
• On the motion of concentrated defects in elastic media
• Statistical theory of dislocations
• Groups of diffeomorphisms and the motion of an incompressible fluid
• Completely integrable systems and symplectic actions
• Magnetohydrodynamical model of pulsar rotation. Exact periodic solutions
• Hamiltonian group actions and dynamical systems of calogero type
• The Mechanics of the Homogeneously‐Deformable Body. Dynamical Models with High Symmetries

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