We consider, after Albouy–Moeckel, the inverse problem for collinear central configurations: Given a collinear configuration of n bodies, find positive masses which make it central. We give some new estimates concerning the positivity of Albouy–Moeckel Pfaffians: We show that for any homogeneity α and n≤ 6 or n≤ 10 and α= 1 (computer assisted) the Pfaffians are positive. Moreover, for the inverse problem with positive masses, we show that for any homogeneity and n≥ 4 there are explicit regions of the configuration space without solutions of the inverse problem.

Ferrario, D. (2020). Pfaffians and the inverse problem for collinear central configurations. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 132(6-7) [10.1007/s10569-020-09975-3].

Pfaffians and the inverse problem for collinear central configurations

Ferrario D. L.
2020

Abstract

We consider, after Albouy–Moeckel, the inverse problem for collinear central configurations: Given a collinear configuration of n bodies, find positive masses which make it central. We give some new estimates concerning the positivity of Albouy–Moeckel Pfaffians: We show that for any homogeneity α and n≤ 6 or n≤ 10 and α= 1 (computer assisted) the Pfaffians are positive. Moreover, for the inverse problem with positive masses, we show that for any homogeneity and n≥ 4 there are explicit regions of the configuration space without solutions of the inverse problem.
Articolo in rivista - Articolo scientifico
Central configuration; Inverse problem; n-Body problem; Pfaffian
English
13-lug-2020
2020
132
6-7
32
none
Ferrario, D. (2020). Pfaffians and the inverse problem for collinear central configurations. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 132(6-7) [10.1007/s10569-020-09975-3].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/297040
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