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This article is cited in 1 scientific paper (total in 1 paper)
Mathematical problems of nonlinearity
On a Class of Precessions of a Rigid Body
with a Fixed Point under the Action of Forces
of Three Homogeneous Force Fields
G. V. Gorr Steklov Mathematical Institute of Russian Academy of Science,
ul. Gubkina 8, Moscow, 119991 Russia
Abstract:
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.
Keywords:
three homogeneous force fields, precessions, dynamically symmetric bodies, elliptic functions.
Received: 20.05.2023 Accepted: 22.06.2023
Citation:
G. V. Gorr, “On a Class of Precessions of a Rigid Body
with a Fixed Point under the Action of Forces
of Three Homogeneous Force Fields”, Rus. J. Nonlin. Dyn., 19:2 (2023), 249–264
Linking options:
https://www.mathnet.ru/eng/nd851 https://www.mathnet.ru/eng/nd/v19/i2/p249
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