Central Configurations and Mutual Differences
Central configurations are solutions of the equations λmjqj=∂U/∂qj, where U denotes the potential function and each qj is a point in the d-dimensional Euclidean space E≅Rd, for j=1,…,n. We show that the vector of the mutual differences qij=qi−qj satisfies the equation −(λ/α)q=Pm(Ψ(q)), where Pm is t...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2017 |
| ISSN: | 1815-0659 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148595 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Central Configurations and Mutual Differences / D.L. Ferrario // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 17 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Central configurations are solutions of the equations λmjqj=∂U/∂qj, where U denotes the potential function and each qj is a point in the d-dimensional Euclidean space E≅Rd, for j=1,…,n. We show that the vector of the mutual differences qij=qi−qj satisfies the equation −(λ/α)q=Pm(Ψ(q)), where Pm is the orthogonal projection over the spaces of 1-cocycles and Ψ(q)=q/|q|α+2. It is shown that differences qij of central configurations are critical points of an analogue of U, defined on the space of 1-cochains in the Euclidean space E, and restricted to the subspace of 1-cocycles. Some generalizations of well known facts follow almost immediately from this approach.
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| ISSN: | 1815-0659 |