Periodic Solutions and KAM Tori for the Planar Non-Homogeneous Straight Segment

• Angelo Alberti ^[1] ; Claudio Vidal ^[2]
  1. [1] Universidade Federal de Sergipe

     Universidade Federal de Sergipe

     Brasil

     
  2. [2] Universidad del Bío-Bío

     Universidad del Bío-Bío

     Comuna de Concepción, Chile

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 5, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this work we consider the planar motion of an infinitesimal mass attracted by the gravitational force induced by a body modelled as a non-homogeneous straight segment. We consider two situations: the segment can rotate uniformly with angular velocityω = 0, or it is fixed (i.e.,ω = 0). The aim of this paper is to prove the existence of different families of periodic solutions for this problem, such as those obtained via the averaging method for Hamiltonian systems or the continuation method of Poincaré by using a discrete symmetry. We prove the existence of several families of periodic solutions as a continuation of the circular and elliptical orbits of the (fixed or rotating) Kepler problem in the planar case. We also provide information on the linear stability of the periodic solutions. Furthermore, we prove the existence of KAM tori close to some of the previously stable periodic solutions.

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