  In this paper we present a generalization of the Goraychev--Chaplygin
integrable case on a bundle of Poisson brackets, and on Sokolov terms in his
new integrable case of Kirchhoff equations. We also present a new analogous
integrable case for the quaternion form of rigid body dynamics' equations. This
form of equations is recently developed and we can use it for the description
of rigid body motions in specific force fields, and for the study of different
problems of quantum mechanics. In addition we present new invariant relations
in the considered problems.
