A CLASS OF POLYNOMIAL SOLUTIONS IN THE PROBLEM OF THE MOTION OF A GYROSTAT IN A MAGNETIC-FIELD

The conditions for the existence of a class of polynomial solutions of the equations of motion of a gyrostat in a magnetic field are studied taking the Barnett-London effect [1, 2] into account. It is shown tha t if the condition of motion isoconicity is imposed when the moving an d stationary hodographs of the angular velocity are symmetric images o f one another in the plane tangent to them, the problem can be solved completely and yields two new cases of integrability of the equations of motion. (C) 1998 Elsevier Science Ltd. All rights reserved.