In this paper the following fact is proved: the complete characteristic equation of 8-th degree for the closed circular cylindrical shell in Goldenweiser's version (Love-Timoshenko's approach to the change of circumferential curvature) has not real roots for harmonics $n=2$, so that this version is not in contradiction to the law of conservation of energy. If we neglect little members in this equation, real roots appear. Solving this equation, two regions of the numerical instability arise. For the calculation of the roots a) algebraic algol-procedure RADICES, b] iteration method and c) asymptitic series, which is suitable in the instability region, are introduced.
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