It is proven that the completely integrable general Kirchhoff case of the Kirchhoff equations for $B \ne 0$ is not an 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.
Keywords:
Kirchhoff equations, Kirchhoff case, Chaplygin case, algebraic integrable systems
Citation:
Dragović V., Gajić B., On the Cases of Kirchhoff and Chaplygin of the Kirchhoff Equations, Regular and Chaotic Dynamics,
2012, Volume 17, Number 5,
pp. 431-438