On integrability of the Euler-Poisson equations

We consider a special case of the Euler-Poisson system of equations, describing the motion of a rigid body around a fixed point. We find 44 sets of stationary solutions near which the system is locally integrable. Ten of them are real. We also study the number of these complex stationary solutions in 3-dimensional invariant manifolds of the system. We find that the number is 4, 2, 1, or 0. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 1, pp. 45–59, 2007.