[math-fun] three-body (and begin for 4-body) problem with stationary shape; "opposite" jujitsu

Stockton also in another of his pages claims without proof that the 3-body eq.triangle stationary-shape solution is stable if the masses A,B,C obey 27*(A*B+B*C+A*C) < (A+B+C)^3. This was shown by Gascheau in 1843. Stockton cites this paper Bruno Sicardy: Stability of the triangular Lagrange points beyond Gascheau’s value, http://www.lesia.obspm.fr/perso/bruno-sicardy/biblio/biblio/Sicardy_Gascheau... which shows the stability problem is really quite deep and nasty! -- and J M A Danby: The Stability of the Triangular Lagrangian Points in the General Problem of Three Bodies, The Astronomical Journal 69.4 (1964) 294-296.