Journal title RENDICONTI
Author/s Antonio Giorgilli, Ugo Locatelli, Marco Sansottera
Publishing Year 2026 Issue 2025/2
Language Italian Pages 26 P. 145-170 File size 0 KB
DOI 10.3280/rndoa2025oa21163
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We revisit the problem of collinear solutions of the problem of N bodies, as investigated by Euler and Lagrange. Unlike most existing studies, we consider a general class of attractive forces. In this respect, we follow Newton's attitude in Principia of first con-sidering the problem in its generality, without assuming that the force obeys the gravitational inverse square law. We find that circular concentric orbits, also named relative equilibria, exist as a general fact. Conversely, we show that homographic orbits o exist only for forces that obey a power law.
Antonio Giorgilli, Ugo Locatelli, Marco Sansottera, COrbite omografiche collineari nel problema generale dei N corpi in "RENDICONTI" 2/2025, pp 145-170, DOI: 10.3280/rndoa2025oa21163