130495 20240125162931.0 doi 10.1016/j.amc.2013.10.029 sideral 83302 ART-2013-83302 eng Tresaco, Eva (orcid)0000-0003-4859-7224 Numerical analysis of periodic solutions and bifurcations in the planetary annulus problem 2013 This paper discusses the dynamics of particles orbiting planetary rings under a general central potential. Starting with the mathematical description of the dynamical system, we analyze the motion of a particle with infinitesimal mass as attracted by a central body surrounded by a homogeneous circular annular disk. Throughout the paper we carry out an analytic search of the most relevant equilibria solutions and, based on that, we investigate numerically the stability matrix of the system to find stability inequalities. In this way, we describe the in-plane and out-of-plane motion by means of the numerical continuation of a wide number of uni-parametric families of planar and spatial periodic orbits. We present a description of the main families of periodic orbits encountered, their bifurcations and linear stability. With the aim of reproducing a more realistic scenario, we analyse different mass proportions between the annulus and the central body, we consider an oblate planet and we also include a composition of rings in the dynamical model. info:eu-repo/grantAgreement/ES/MINECO/AYA2008- 05572 info:eu-repo/semantics/closedAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 1.6 2013 MATHEMATICS, APPLIED 30 / 251 = 0.12 2013 Q1 T1 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Riaguas, Andrés (orcid)0000-0001-6097-1202 Elipe, Antonio Universidad de Zaragoza (orcid)0000-0001-5208-4494 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 225 (2013), 645-655 Appl. math. comput. Applied Mathematics and Computation 0096-3003 4913428 http://zaguan.unizar.es/record/130495/files/texto_completo.pdf Postprint 2114219 http://zaguan.unizar.es/record/130495/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:130495 articulos driver 2024-01-25-15:15:20 ARTICLE