On the full list of finite-valued solutions of the Euler-Poisson equations having four first integrals

摘要

Only 13 general and partial solutions of the problem of a heavy rigid body's movement have been found from the discovery of the first one by Euler in 1758 till now. All these solutions are finite-valued in the classical Euler and Poisson's variables except the one in the Hess case. In this paper the problem of finding the full list of the finite-valued solutions is considered.