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We solved the Poisson equations, obtaining their exact solution in elementaryfunctions for the rotation matrix of a free asymmetrical body with angularvelocity vector lying on separatrices. This allows us to discuss the temporalevolution of Dzhanibekov's nut directly in the Laboratory system, where it isobserved. The rotation matrix depends on two parameters with clear physicalinterpretation as a frequency and a damping factor of the solution. Qualitativeanalysis of the solution shows that it properly describe a single-jumpDzhanibekov effect.

An asymmetrical body: example of analytical solution for the rotation matrix in elementary functions and Dzhanibekov effect