An integrable system related to the spherical top and the Toda chain (Q5941963)

The motion over the sphere \(S^2\) with the potential \(V=(x_1x_2x_3)^{-2/3}\) is known to be completely integrable, possessing an additional first integral that is cubic in momenta. In this paper the Lax representation without a spectral parameter is obtained via a comparison with the Neumann system and a Kovalevskaya-Painlevé analysis is given through a comparison with three-particle Toda chain.