Central configurations are solutions of the equations (formula presented), 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 (formula presented) satisfies the equation (formula presented), where Pm is the orthogonal projection over the spaces of 1-cocycles and (formula presented). 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.
Ferrario, D. (2017). Central Configurations and Mutual Differences. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 13, 1-11 [10.3842/SIGMA.2017.021].
Citazione: | Ferrario, D. (2017). Central Configurations and Mutual Differences. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 13, 1-11 [10.3842/SIGMA.2017.021]. | |
Tipo: | Articolo in rivista - Articolo scientifico | |
Carattere della pubblicazione: | Scientifica | |
Presenza di un coautore afferente ad Istituzioni straniere: | No | |
Titolo: | Central Configurations and Mutual Differences | |
Autori: | Ferrario, D | |
Autori: | FERRARIO, DAVIDE LUIGI (Corresponding) | |
Data di pubblicazione: | 2017 | |
Lingua: | English | |
Rivista: | SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.3842/SIGMA.2017.021 | |
Appare nelle tipologie: | 01 - Articolo su rivista |
File in questo prodotto:
File | Descrizione | Tipologia | Licenza | |
---|---|---|---|---|
sigma17-021.pdf | Publisher's version | Administrator Richiedi una copia |