This question for the case of a homogeneous field—the field of gravity—was discussed in detail by Prof. M.I. Akimov, who found all surfaces that permit the motion of apoint mass under gravity along helical lines with a vertical axis in the presence of friction, and investigated the conditions for these surfaces under which the motion in question would be stable.

In this paper is examined a general case of the small vibrations of the inertial screen considered as a rigid body possessing all the 6 degrees of liberty. There are also determined the conditions under which the problem can be reduced to three degrees of liberty (the case examined in a previous paper entitled "Upon inertial screens"). Euler’s equations determining the motion of a rigid body are simplified considering the smallness of its vibrations and in the first approximation the problem is reduced to the solution of a system of 6 simultaneous linear equations with constant coefficients, or even to separate linear equations. In case of need the result can be improved by consecutive approximations taking also non-linear equations into consideration.