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For the Kowalevski gyrostat change of variables similar to that of theKowalevski top is done. We establish one to one correspondence between theKowalevski gyrostat and the Clebsch system and demonstrate that Kowalevskivariables for the gyrostat practically coincide with elliptic coordinates onsphere for the Clebsch case. Equivalence of considered integrable systemsallows to construct two Lax matrices for the gyrostat using known rational andelliptic Lax matrices for the Clebsch model. Associated with these matricessolutions of the Clebsch system and, therefore, of the Kowalevski gyrostatproblem are discussed. The Kotter solution of the Clebsch system in modernnotation is presented in detail.Comment: LaTeX, 24 page

On a trajectory isomorphism of the Kowalevski gyrostat and the Clebsch problem