Systems of Hess-Appel'rot type

Abstract

We construct higher-dimensional generalizations of the classical Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of this new class of systems, which is closely related to the integration of the Lagrange bitop performed by us recently and uses Mumford relation for theta divisors of double unramified coverings. Based on the basic properties satisfied by such a class of systems related to bi-Poisson structure, quasi-homogeneity, and conditions on the Kowalevski exponents, we suggest an axiomatic approach leading to what we call the "class of systems of Hess-Appel'rot type".

40 pages. Comm. Math. Phys. (to appear)

References in corpus (2)

• The complex geometry of Lagrange top
• The Lagrange bitop on so(4) x so(4) and geometry of the Prym varieties

Cited by in corpus (7)

• Symmetries and Integrability
• Contact flows and integrable systems
• Generalization and Geometrization of the Kowalevski top
• On the Cases of Kirchhoff and Chaplygin of the Kirchhoff Equations
• The rigid body dynamics: classical and algebro-geometric integration
• Partial Reductions of Hamiltonian Flows and Hess-Appel'rot Systems on SO(n)
• Elliptic Curves and a New Construction of Integrable Systems