Mechanics of Solids (about journal) Mechanics of Solids
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IssuesArchive of Issues2022-5pp.1059-1067

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E.A. Nikonova, "Stationary Motions of a Close to Regular Isosceles Tetrahedron with a Fixed Point in the Central Newtonian Force Field," Mech. Solids. 57 (5), 1059-1067 (2022)
Year 2022 Volume 57 Number 5 Pages 1059-1067
DOI 10.3103/S0025654422050211
Title Stationary Motions of a Close to Regular Isosceles Tetrahedron with a Fixed Point in the Central Newtonian Force Field
Author(s) E.A. Nikonova (Federal Research Center "Computer Science and Control" of the RAS, Moscow, 119333 Russia, nikonova.ekaterina.a@gmail.com)
Abstract The existence, stability, and branching of stationary motions of a tetrahedral body around a fixed point in the central Newtonian force field are studied. The case of an isosceles tetrahedron close to regular is considered. The connection of these properties of stationary motions with the properties of stationary motions of a regular tetrahedron is investigated. In celestial mechanics, the gravitational field of an irregularly shaped celestial body is often modeled by the gravitational field of some set of massive points. Representations in the form of a set of two or three point masses contain symmetries that are not inherent in real bodies. Approximations of gravitational fields with the help of fields of attraction of exactly four massive points seem to be the most suitable.
Keywords rigid body with a fixed point, body in a central gravitational field, Routh theory, stability and branching of stationary motions, isosceles tetrahedron
Received 14 December 2021Revised 06 January 2022Accepted 07 January 2022
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