On a Class of Precessions of a Rigid Body with a Fixed Point under the Action of Forces of Three Homogeneous Force Fields
Received 20 May 2023; accepted 22 June 2023; published 30 June 2023
2023, Vol. 19, no. 2, pp. 249-264
Author(s): Gorr G. V.
This paper is concerned with a special class of precessions of a rigid body having a fixed
point in a force field which is a superposition of three homogeneous force fields. It is assumed
that the velocity of proper rotation of the body is twice as large as its velocity of precession. The
conditions for the existence of the precessions under study are written in the form of a system of
algebraic equations for the parameters of the problem. Its solvability is proved for a dynamically
symmetric body. It is proved that, if the ellipsoid of inertia of the body is a sphere, then the
nutation angle is equal to $\arccos \frac{1}{3}$. The resulting solution of the equations of motion of the body
is represented as elliptic Jacobi functions.
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