Displaying similar documents to “Integrable Hamiltonian systems on Lie groups: Kowalewski type.”

Integrable three-dimensional coupled nonlinear dynamical systems related to centrally extended operator Lie algebras and their Lax type three-linearization

J. Golenia, O. Hentosh, A. Prykarpatsky (2007)

Open Mathematics

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The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integro-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Bäcklund transformation. The connection of this hierarchy with integrable by Lax two-dimensional Davey-Stewartson type systems is studied.

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...

On the mobility and efficiency of mechanical systems

Gershon Wolansky (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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It is shown that self-locomotion is possible for a body in Euclidian space, provided its dynamics corresponds to a non-quadratic Hamiltonian, and that the body contains at least 3 particles. The efficiency of the driver of such a system is defined. The existence of an optimal (most efficient) driver is proved.