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One Class of Resonance Precession Motions of a Rigid Body under the Action of Three Homogeneous Force Fields
- Authors: Gorr G.V.1
-
Affiliations:
- State Budgetary Institution “Institute of Applied Mathematics and Mechanics”
- Issue: Vol 87, No 1 (2023)
- Pages: 3-18
- Section: Articles
- URL: https://journals.rcsi.science/0032-8235/article/view/138820
- DOI: https://doi.org/10.31857/S0032823523010071
- EDN: https://elibrary.ru/HVLUQK
- ID: 138820
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Abstract
The article is devoted to the problem on motion of a rigid body with a fixed point under the action of a force field, which is the superposition of three homogeneous force fields. Existence conditions are investigated for precession motions, which are characterized by the following property: the angular velocity of the precession of the body is two times more than the angular velocity of its proper rotation. It is established that the body has the dynamic symmetry with respect to an axis making a constant angle with a vector fixed in the immovable space. In the case of the body with the spherical mass distribution this angle equals to \({\text{arccos}}\frac{1}{4}\). Solution of the equations of motion of the body is expressed through the elliptic functions of time.
About the authors
G. V. Gorr
State Budgetary Institution “Institute of Applied Mathematics and Mechanics”
Author for correspondence.
Email: gvgorr@gmail.com
Russia, Donetsk
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