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In machine dynamics the balancing of gyroscopic system has a long tradition. In many textbooks the contributions to this topic are made regarding rigid gyroscope (see e.g. Huyen P., Mau N. T. [1-4)). The problems related to elastic multibody systems are more complicated. A good survey of recent results was presented by Anperin L. B. [5), Mau N. T. [6). In a balancing problem usually there is asymptotic feature. However, in results of authors there are centenary elements. So a time expand, the balancing nature of gyroscopic system has been destroying. In this paper author considers the balanced gyroscope with elastic symmetric axes on the mobile basis. The equations of motion of gyroscope have been represented in uncountable by degree units. The differential equation system is coming to the standard form, which can be solve by the method of separation motion. Computed result is the exponential function so centenary element destroyed.

Strengthening balance of motion of gyroscope on mobile basis