 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| S.G. Zhuravlev, "Homothetic radial solutions of the Newtonian general spatial (N+1)-body problem," J. Appl. Math. Mech. 80 (1), 33-36 (2016) |
| Year |
2016 |
Volume |
80 |
Issue |
1 |
Pages |
33-36 |
| DOI |
10.1016/j.jappmathmech.2016.05.006 |
| Title |
Homothetic radial solutions of the Newtonian general spatial (N+1)-body problem |
| Author(s) |
S.G. Zhuravlev (Moscow Automobile and Road Construction University, Moscow, Russia, sergio2009@yandex.ru) |
| Abstract |
The equations of motion are derived, and the existence of symmetrical radial solutions of the general spatial (N+1)-body problem, in which N bodies of identical mass m are found at the initial instant of time at the vertices of polyhedrons known as Platonic bodies (N = 4, 6, 8, 12, 20) and the (N+1)-th body of mass M is found at the geometrical centre of the polyhedron, is proved rigorously, analytically and numerically. It is assumed that all the bodies are attracted according to Newton's law and that the initial velocities of the bodies with mass m are directed along a radius vector. The solutions found are homothetically expanding (contracting) central configurations. A geometrical image of the solutions is presented for a hexahedron, and their evolution is described for all the Platonic bodies. A distinguishing characteristic of the solutions is the value of the rate of expansion (contraction) of a configuration, which depends on the attraction law, the number of vertices in the polyhedron and its configuration. |
| Received |
17 September 2014 |
| Link to Fulltext |
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