About motion of symmetric gyrostat with a variable gyrostatic moment in two tasks of dynamics

G. V. Gorr^a, A. V. Maznev<sup>b

a</sup> Institute of Applied Mathematics and Mechanics of NASU, R. Luxembourg 74, Donetsk, 83114, Ukraine
^b Donetsk National University, Universitetskaya 24, Donetsk, 83055, Ukraine

Abstract: The motion of symmetric gyrostat with a variable gyrostatic moment in two tasks of dynamics: in a task about motion of gyrostat under the action of potential and gyroscopic forces and in a task about motion of gyrostat in the magnetic field taking into account the effect of Barnett–London is considered. The decisions of equalizations which contain six arbitrary permanent are indicated.

Keywords: symmetric gyrostat, equalizations of Kirchhoff–Poisson, effect of Barnett–London.

UDC: 531.38

MSC: 70E17, 70E40

Received: 14.10.2011
Accepted: 22.05.2012