Avoiding collisions under topological constraints in variational problems coming from celestial mechanics

2014/04/09 by Nicola Soave, Susanna Terracini, Soave, Nicola +1
Mathematics · #37N05 #70F10 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37N05 #msc:70F10

paper · pdf · doi:10.48550/arxiv.1404.2490

32 pages

arxiv created 2014/04/09 · arxiv updated 2014/04/10

Abstract

In a singular potential setting, we generalize a method which allows to show that minimizers under topological constraints of the action functional (or of the Maupertuis') are collision-free. This methods applies to 3-dimensional problems of celestial mechanics exhibiting a particular cylindrical symmetry, as well as to planar problems of N-centre type, where it gives optimal results.

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