We study the relative equilibria of the limit case of the pla-
nar Newtonian 4{body problem when three masses tend to zero, the
so-called (1 + 3){body problem. Depending on the values of the in-
nitesimal masses the number of relative equilibria varies from ten to
fourteen. Always six of these relative equilibria are convex ...»»»»
We study the relative equilibria of the limit case of the pla-
nar Newtonian 4{body problem when three masses tend to zero, the
so-called (1 + 3){body problem. Depending on the values of the in-
nitesimal masses the number of relative equilibria varies from ten to
fourteen. Always six of these relative equilibria are convex and the oth-
ers are concave. Each convex relative equilibrium of the (1 + 3){body
problem can be continued to a unique family of relative equilibria of the
general 4{body problem when three of the masses are su ciently small
and every convex relative equilibrium for these masses belongs to one of
these six families.^^^^
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(c) Society for Industrial and Applied Mathematics
Citació Bibliogràfica:
Corbera, M., Cors, J., Llibre, J., & Moeckel, R. (2015). Bifurcation of relative equilibria of the (1+3)-body problem. SIAM Journal on Mathematical Analysis, 47(2), 1377-1404.