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We aim to completely formalize the rough topological analysis of integrableHamiltonian systems admitting analytical solutions such that the initial phasevariables along with the time derivatives of the auxiliary variables areexpressed as rational functions (in fact, as polynomials) in some set ofradicals depending on one variable each. We suggest a method to define theadmissible regions in the integral constants space, the segments of oscillationof the separated variables and the number of connected components of integralmanifolds and critical integral surfaces. This method is based on somealgorithms of processing the tables of some Boolean vector-functions and ofreducing the matrices of linear Boolean vector-functions to some canonicalform. From this point of view we consider here the topologically richestclassical problems of the rigid body dynamics. The article will be continuedwith the investigation of some new integrable problems.

Topological analysis and Boolean functions. I. Methods and application to classical systems