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.
Citazione: | Ferrario, D. (2017). Central Configurations and Mutual Differences. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 13, 1-11. |
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 |