The paper deals with problems concerning power gyroscopes for stabilization of vibro-izolation system. Two variants of gyro support with air drive were designed, namely with gas bearings and precision rolling bearings. Precession frame of the gyro is supported in aerostatic journal bearings to achieve minimum passive resistance. Some special phenomena, such as pneumatic instalibity, were found in some test regimes both at aerostatic thrust bearing of gyro support and aerostatic journal bearings of the frame support. However, with air inlet pressure level limited to value required for proper function of bearings, no instability was encountered.
Classical Kloosterman sums have a prominent role in the study of automorphic forms on GL$_2$ and further they have numerous applications in analytic number theory. In recent years, various problems in analytic theory of automorphic forms on GL$_3$ have been considered, in which analogous GL$_3$-Kloosterman sums (related to the corresponding Bruhat decomposition) appear. In this note we investigate the first four power-moments of the Kloosterman sums associated with the group SL$_3(\mathbb Z)$. We give formulas for the first three moments and a nontrivial bound for the fourth.