149741 20251017144546.0 doi 10.1007/s10569-015-9651-2 sideral 92254 ART-2015-92254 eng Dena, Á. (orcid)0000-0002-1029-0764 Efficient computational approaches to obtain periodic orbits in Hamiltonian systems: application to the motion of a lunar orbiter 2015 Access copy available to the general public Unrestricted In this paper, we study the problem of computing periodic orbits of Hamiltonian systems providing large families of such orbits. Periodic orbits constitute one of the most important invariants of a system, and this paper provides a comprehensive analysis of two efficient computational approaches for Hamiltonian systems. First, a new version of the grid search method, applied to problems with three degrees of freedom, has been considered to find, systematically, symmetric periodic orbits. To obtain non-symmetric periodic orbits, we use a modification of an optimization method based on an evolutionary strategy. Both methods require a great computational effort to find a big number of periodic orbits, and we apply parallelization tools to reduce the CPU time. Finally, we present a strategy to provide initial conditions of the periodic orbits with arbitrary precision. We apply all these algorithms to the problem of the motion of the lunar orbiter referred to the rotating reference frame of the Moon. The periodic orbits of this problem are very useful from the space engineering point of view because they provide low-cost orbits. info:eu-repo/grantAgreement/EC/FP7/ 228398/EU/Pan-European Research infrastructure on High Performance Computing for 21st century Science/HPC-EUROPA2 info:eu-repo/grantAgreement/ES/MICINN/MTM2012-31883 info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 1.594 2015 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS 34 / 101 = 0.337 2015 Q2 T2 ASTRONOMY & ASTROPHYSICS 37 / 62 = 0.597 2015 Q3 T2 1.025 2015 Modeling and Simulation 2015 Q1 Mathematical Physics 2015 Q1 Space and Planetary Science 2015 Q2 Astronomy and Astrophysics 2015 Q2 Applied Mathematics 2015 Q2 Computational Mathematics 2015 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Abad, A. Universidad de Zaragoza (orcid)0000-0002-5692-5876 Barrio, R. Universidad de Zaragoza (orcid)0000-0002-8089-343X 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 2004 398 Universidad de Zaragoza Dpto. Física Teórica Área Física de la Tierra 124 (2015), 51-71 Celest. mech. dyn. astron. Celestial Mechanics and Dynamical Astronomy 0923-2958 2057400 http://zaguan.unizar.es/record/149741/files/texto_completo.pdf Postprint 1058088 http://zaguan.unizar.es/record/149741/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:149741 articulos driver 2025-10-17-14:09:40 ARTICLE