We discuss the Poisson structure underlying the two-field Kowalevski gyrostat and the Kowalevski top. We start from their Lax structure and construct a suitable pencil of Poisson brackets which endows these systems with the structure of bi-Hamiltonian completely integrable systems. We study the Casimir functions of such pencils, and show how it is possible to frame the Kowalevski systems within the so-called Gel'fand-Zakharevich biHamiltonian setting for integrable systems
Falqui, G. (2001). Lax representation and Poisson geometry of the Kowalevski top. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 34(11), 2077-2085 [10.1088/0305-4470/34/11/301].
Lax representation and Poisson geometry of the Kowalevski top
Falqui, G
2001
Abstract
We discuss the Poisson structure underlying the two-field Kowalevski gyrostat and the Kowalevski top. We start from their Lax structure and construct a suitable pencil of Poisson brackets which endows these systems with the structure of bi-Hamiltonian completely integrable systems. We study the Casimir functions of such pencils, and show how it is possible to frame the Kowalevski systems within the so-called Gel'fand-Zakharevich biHamiltonian setting for integrable systems
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
