The stability of regular Grioli precessions

In the plane of two essential parameters of the problem, the region the nec essary and (individually) sufficient conditions of stability of regular Gri oli precessions in the problem of the motion of a heavy, dynamically asymme trical rigid body about a fixed point is defined. The existence of periodic motions close to regular Grioli precessions is also proved. A method that requires only in solutions of the Cauchy problem to calculate the character istic exponents of a reversible linear periodic system of order l + n (l gr eater than or equal to n) is proposed, (C) 2001 Elsevier Science Ltd. All r ights reserved.