A Lax pair for Kowalevski's top (Q1092483)

We show that on each level surface of the invariants, the equations of the Kowalevski top are equivalent to a Neumann system describing the motion of a mass point on the sphere \(S^ 2:| p| =1\) under the influence of a force -Qp. This allows us to write a global Lax pair for the Kowalevski system and to show that Kowalevski's original reduction of the integration of the equations of motion to Jacobi's inversion theorem is identical to the introduction of ``elliptical spherical coordinates'' for integrating C. Neumann's system.