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Bifurcation of relative equilibria of the (1+3)-body problem

Bifurcation of relative equilibria of the (1+3)-body problem
 
Corbera Subirana, Montserrat ; Cors Iglesias, Josep Maria ; Llibre, Jaume ; Moeckel, Richard
2015

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Enllaç permanent: http://hdl.handle.net/10854/4046
 
Versió de l'editor: https://doi.org/10.1137/140978661
 

Abstract

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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Citation:

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.