On the Cases of Kirchhoff and Chaplygin of the Kirchhoff Equations

Abstract

It is proven that the general Kirchhoff case of the Kirchhoff equations for $B\ne 0$ is not algebraic complete integrable system. Similar analytic behavior of the general solution of the Chaplygin case is detected. Four-dimensional analogues of the Kirchhoff and the Chaplygin cases are defined on $e(4)$ with the standard Lie-Poisson bracket.

References in corpus (3)

• Systems of Hess-Appel'rot type
• Prym varieties and applications
• Systems of Hess-Appel'rot Type and Zhukovskii Property

Cited by in corpus (3)

• The rigid body dynamics: classical and algebro-geometric integration
• Lie bundle on the space of deformed skew-symmetric matrices
• Poisson brackets after Jacobi and Plucker