Displaying similar documents to “Symmetries and Integrability”

The Lagrange rigid body motion

Tudor Ratiu, P. van Moerbeke (1982)

Annales de l'institut Fourier

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We discuss the motion of the three-dimensional rigid body about a fixed point under the influence of gravity, more specifically from the point of view of its symplectic structures and its constants of the motion. An obvious symmetry reduces the problem to a Hamiltonian flow on a four-dimensional submanifold of s o ( 3 ) × s o ( 3 ) ; they are the customary Euler-Poisson equations. This symplectic manifold can also be regarded as a coadjoint orbit of the Lie algebra of the semi-direct product group S O ( 3 ) × s o ( 3 ) with...

Linearization of Poisson actions and singular values of matrix products

Anton Alekseev, Eckhard Meinrenken, Chris Woodward (2001)

Annales de l’institut Fourier

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We prove that the linearization functor from the category of Hamiltonian K -actions with group-valued moment maps in the sense of Lu, to the category of ordinary Hamiltonian K - actions, preserves products up to symplectic isomorphism. As an application, we give a new proof of the Thompson conjecture on singular values of matrix products and extend this result to the case of real matrices. We give a formula for the Liouville volume of these spaces and obtain from it a hyperbolic version...