In this work, we prove the existence of solutions for the double choreographical n-body problem as critical points which are not minimizers of the corresponding Lagrangian action functional. We use the topological features of the sublevels of the action when a strong force assumption is imposed. We conclude with a description of an operative method to determine these solutions in R-3.
Barutello, V., Terracini, S. (2006). Double choreographical solutions for n-body type problems. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 95(1-4), 67-80 [10.1007/s10569-006-9030-0].
Double choreographical solutions for n-body type problems
TERRACINI, SUSANNA
2006
Abstract
In this work, we prove the existence of solutions for the double choreographical n-body problem as critical points which are not minimizers of the corresponding Lagrangian action functional. We use the topological features of the sublevels of the action when a strong force assumption is imposed. We conclude with a description of an operative method to determine these solutions in R-3.
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