The quasi-bi-Hamiltonian formulation of the Lagrange top

Abstract

Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the possible reductions of the Poisson tensors, the vector field and its Hamiltonian functions on a four-dimensional space. We show that the vector field of the Lagrange top possesses, on the reduced phase space, a quasi-bi-Hamiltonian formulation, which provides a set of separation variables for the corresponding Hamilton-Jacobi equation.

12 pages, no figures, LaTeX, to appear in J. Phys. A: Math. Gen. (March 2002)

References in corpus (4)

• Quasi-BiHamiltonian Systems and Separability
• Reduction of bihamiltonian systems and separation of variables: an example from the Boussinesq hierarchy
• Bihamiltonian geometry and separation of variables for Toda lattices
• Bi-Hamiltonian manifolds, quasi-bi-Hamiltonian systems and separation variables

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• Poisson Pencils, Integrability, and Separation of Variables
• Towards a classification of natural bi-hamiltonian systems
• Haantjes Algebras of the Lagrange Top
• A Note on the Rotationally Symmetric SO(4) Euler Rigid Body
• A geometric approach to the separability of the Neumann-Rosochatius system
• Deformation of algebroid bracket of differential forms and Poisson manifold