Application of generalized differential Euler-Gess equations in rigid body and gyrostat dynamics

This paper deals with the generalized differential dynamic equations of the Euler-Hess form, which contain an arbitrary three-dimensional vector. From generalized equations we can obtain classical equation of Hess and new forms of dynamic equations in the Euler-Gess form without direction cosines of the vertical. The integrable vector equation in the Euler-Gess form is received. The new solution of the Poisson equation in elliptic functions in Euler case is discovered. Vector and quaternion parameters of a rigid body orientation on vertical direction cosines are determined.