Steklov-Lyapunov type systems
In this paper we describe integrable generalizations of the classical Steklov– Lyapunov systems, which are defined on a certain product so(m) × so(m), as well as the structure of rank r coadjoint orbits in so(m)×so(m). We show that the restriction of these systems onto some subvarieties of the orbits...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2003 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/900 |
| Acceso en línea: | https://hdl.handle.net/2117/900 |
| Access Level: | acceso abierto |
| Palabra clave: | Hamiltonian dynamical systems Lagrangian functions Dynamics Hamiltonian systems Steklov-Lyapunov systems Hamilton, Sistemes de Lagrange, Funcions de Dinàmica de cossos rígids Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::70 Mechanics of particles and systems::70E Dynamics of a rigid body and of multibody systems Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics |
| Sumario: | In this paper we describe integrable generalizations of the classical Steklov– Lyapunov systems, which are defined on a certain product so(m) × so(m), as well as the structure of rank r coadjoint orbits in so(m)×so(m). We show that the restriction of these systems onto some subvarieties of the orbits written in new matrix variables admits a new r × r matrix Lax representation in a generalized Gaudin form with a rational spectral parameter. In the case of rank 2 orbits a corresponding 2 × 2 Lax pair for the reduced systems enables us to perform a separation of variables. |
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