On bi-hamiltonian geometry of the Lagrange top

Abstract

We consider three different incompatible bi-Hamiltonian structures for the Lagrange top, which have the same foliation by symplectic leaves. These bivectors may be associated with the different 2-coboundaries in the Poisson-Lichnerowicz cohomology defined by canonical bivector on $e^{\ast }(3)$.

11 pages, LaTeX with AMS fonts

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Cited by in corpus (9)

• Integrable Euler top and nonholonomic Chaplygin ball
• New variables of separation for particular case of the Kowalevski top
• On bi-hamiltonian geometry of some integrable systems on the sphere with cubic integral of motion
• On the generalized integrable Chaplygin system
• On natural Poisson bivectors on the sphere
• Haantjes Algebras of the Lagrange Top
• The Harmonic Lagrange Top and the Confluent Heun Equation
• Some compatible Poisson structures and integrable bi-Hamiltonian systems on four dimensional and nilpotent six dimensional symplectic real Lie groups
• On the bi-Hamiltonian structure of Bogoyavlensky system on $so(4)$