On the Euler equation: Bi-Hamiltonian structure and integrals in involution

DOI10.1007/BF00416015zbMath0852.58050MaRDI QIDQ1915201

Livio Pizzocchero, Carlo Morosi

Publication date: 9 December 1996

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

integrable systemsbi-Hamiltonian structuresdynamics on Lie algebras

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Free motion of a rigid body (70E15) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items

Lax–Nijenhuis operators for integrable systems ⋮ ON THE STABILITY PROBLEM FOR THE $\mathfrak{so}(5)$ FREE RIGID BODY ⋮ Lie bundle on the space of deformed skew-symmetric matrices ⋮ Canonoid and Poissonoid transformations, symmetries and biHamiltonian structures ⋮ Tangent lifts of bi-Hamiltonian structures ⋮ Algebraic Nijenhuis operators and Kronecker Poisson pencils ⋮ Stability of equilibria for the \(\mathfrak{so}(4)\) free rigid body ⋮ Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type ⋮ On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian. ⋮ The \(U(n)\) free rigid body: integrability and stability analysis of the equilibria ⋮ Linear bundles of Lie algebras and their applications ⋮ Compatible Lie algebroids and the periodic Toda lattice ⋮ Studies of the Hoyer system. ⋮ Optimal control of the sphere \(S^n\) rolling on \(E^n\) ⋮ Bi-Hamiltonian systems of deformation type ⋮ Classical and quantum dynamics for an extended free rigid body ⋮ TRI–HAMILTONIAN VECTOR FIELDS, SPECTRAL CURVES AND SEPARATION COORDINATES ⋮ Kronecker webs, bihamiltonian structures, and the method of argument translation ⋮ Bi-Hamiltonian manifolds, quasi-bi-Hamiltonian systems and separation variables ⋮ A class of integrable flows on the space of symmetric matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Completely integrable systems, Euclidean Lie algebras, and curves
• Note on the integration of Euler's equations of the dynamics of an \(n\)-dimensional rigid body
• Hamiltonian systems connected with the rotation group
• Integral geodesics of a flow on Lie groups
• A characteristic property of the inertial tensor of a multidimensional solid body
• A simple model of the integrable Hamiltonian equation
• EULER EQUATIONS ON FINITE-DIMENSIONAL LIE GROUPS