 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12949 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8096
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| In English (Mech. Solids): | | 4853 |
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| E.A. Nikonova, "On the Maxwell Representation of the Gravitational Potential for a Symmetric Body," Mech. Solids. 59 (4), 1881-1889 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
4 |
Pages |
1881-1889 |
| DOI |
10.1134/S0025654424602891 |
| Title |
On the Maxwell Representation of the Gravitational Potential for a Symmetric Body |
| Author(s) |
E.A. Nikonova (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, 119333 Russia, nikonova.ekaterina.a@gmail.com) |
| Abstract |
The article analyzes an approach that goes back to Maxwell to the representation of a potential, in particular, the potential of the Newtonian field of gravity as a sum of potentials of multipoles of
different orders. Critical cases of the algorithm for finding the parameters of a multipole, namely, its
axes and moment, are indicated. The cases take place when the body has certain symmetries in the mass distribution. Recommendations for overcoming the identified difficulties are formulated. For a
body with a triaxial ellipsoid of inertia, explicit expressions for the axes and moment of a second-order
multipole that are expressed via second-order inertia integrals are given. It is shown that the axes of the
multipole are orthogonal to the circular cross-sections of the ellipsoid of inertia of the body. Critical cases of calculating a third-order multipole are considered using the example of a model body with
constant density, that has the shape of an equihedral tetrahedron. A method for calculating the axes and moment of a third-order multipole for such a body is given. |
| Keywords |
gravitational potential, moments of inertia integrals of higher orders, Maxwell representation of potential, multipole, isosceles tetrahedron |
| Received |
31 December 2023 | Revised |
16 February 2024 | Accepted |
20 February 2024 |
| Link to Fulltext |
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