Central Configurations and Mutual Differences
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Central Configurations and Mutual Differences
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| Creator |
Ferrario, D.L.
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| Description |
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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| Date |
2019-02-18T16:25:23Z
2019-02-18T16:25:23Z 2017 |
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| Type |
Article
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| Identifier |
Central Configurations and Mutual Differences / D.L. Ferrario // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 17 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 37C25; 70F10 DOI:10.3842/SIGMA.2017.021 http://dspace.nbuv.gov.ua/handle/123456789/148595 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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