Search results for "n-body problem"
showing 3 items of 3 documents
Classical and relativistic n-body problem: from Levi-Civita to the most advanced interplanetary missions
2022
The n-body problem is one of the most important issue in Celestial Mechanics. This article aims to retrace the historical and scientific events that led the Paduan mathematician, Tullio Levi-Civita, to deal with the problem first from a classic and then a relativistic point of view. We describe Levi-Civita's contributions to the theory of relativity focusing on his epistolary exchanges with Einstein, on the problem of secular acceleration and on the proof of Brillouin's cancellation principle. We also point out that the themes treated by Levi-Civita are very topical. Specifically, we analyse how the mathematical formalism used nowadays to test General Relativity can be found in Levi-Civita'…
Integrability and Non Integrability of Some n Body Problems
2016
International audience; We prove the non integrability of the colinear 3 and 4 body problem, for any positive masses. To deal with resistant cases, we present strong integrability criterions for 3 dimensional homogeneous potentials of degree −1, and prove that such cases cannot appear in the 4 body problem. Following the same strategy, we present a simple proof of non integrability for the planar n body problem. Eventually, we present some integrable cases of the n body problem restricted to some invariant vector spaces.
Il problema degli n-corpi in relatività generale
2019
Questa riproposizione in italiano dell’ultimo lavoro di Tullio Levi-Civita (1873- 1941) nasce da una esigenza culturale forte. Nel 2018 Padova e la sua Università hanno celebrato il loro grande scienziato con un importante convegno, accompagnato dalla ristampa di una selezione di suoi lavori, comprendente la sua tesi di laurea autografa. L’ultimo suo lavoro scientifico, “Le problème des n corps en relativité générale”, fu redatto in francese, e per le note vicende risalenti all’abominia fascista delle leggi razziali, fu stampato solo postumo, nel 1950, a cura dell’Accademia delle Scienze di Parigi.