| Home > Articles > Efficient computational approaches to obtain periodic orbits in Hamiltonian systems: application to the motion of a lunar orbiter > MARC |
000149741 001__ 149741 000149741 005__ 20251017144546.0 000149741 0247_ $$2doi$$a10.1007/s10569-015-9651-2 000149741 0248_ $$2sideral$$a92254 000149741 037__ $$aART-2015-92254 000149741 041__ $$aeng 000149741 100__ $$0(orcid)0000-0002-1029-0764$$aDena, Á. 000149741 245__ $$aEfficient computational approaches to obtain periodic orbits in Hamiltonian systems: application to the motion of a lunar orbiter 000149741 260__ $$c2015 000149741 5060_ $$aAccess copy available to the general public$$fUnrestricted 000149741 5203_ $$aIn this paper, we study the problem of computing periodic orbits of Hamiltonian systems providing large families of such orbits. Periodic orbits constitute one of the most important invariants of a system, and this paper provides a comprehensive analysis of two efficient computational approaches for Hamiltonian systems. First, a new version of the grid search method, applied to problems with three degrees of freedom, has been considered to find, systematically, symmetric periodic orbits. To obtain non-symmetric periodic orbits, we use a modification of an optimization method based on an evolutionary strategy. Both methods require a great computational effort to find a big number of periodic orbits, and we apply parallelization tools to reduce the CPU time. Finally, we present a strategy to provide initial conditions of the periodic orbits with arbitrary precision. We apply all these algorithms to the problem of the motion of the lunar orbiter referred to the rotating reference frame of the Moon. The periodic orbits of this problem are very useful from the space engineering point of view because they provide low-cost orbits. 000149741 536__ $$9info:eu-repo/grantAgreement/EC/FP7/ 228398/EU/Pan-European Research infrastructure on High Performance Computing for 21st century Science/HPC-EUROPA2$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2012-31883 000149741 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000149741 590__ $$a1.594$$b2015 000149741 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b34 / 101 = 0.337$$c2015$$dQ2$$eT2 000149741 591__ $$aASTRONOMY & ASTROPHYSICS$$b37 / 62 = 0.597$$c2015$$dQ3$$eT2 000149741 592__ $$a1.025$$b2015 000149741 593__ $$aModeling and Simulation$$c2015$$dQ1 000149741 593__ $$aMathematical Physics$$c2015$$dQ1 000149741 593__ $$aSpace and Planetary Science$$c2015$$dQ2 000149741 593__ $$aAstronomy and Astrophysics$$c2015$$dQ2 000149741 593__ $$aApplied Mathematics$$c2015$$dQ2 000149741 593__ $$aComputational Mathematics$$c2015$$dQ2 000149741 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000149741 700__ $$0(orcid)0000-0002-5692-5876$$aAbad, A.$$uUniversidad de Zaragoza 000149741 700__ $$0(orcid)0000-0002-8089-343X$$aBarrio, R.$$uUniversidad de Zaragoza 000149741 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000149741 7102_ $$12004$$2398$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física de la Tierra 000149741 773__ $$g124 (2015), 51-71$$pCelest. mech. dyn. astron.$$tCelestial Mechanics and Dynamical Astronomy$$x0923-2958 000149741 8564_ $$s2057400$$uhttps://zaguan.unizar.es/record/149741/files/texto_completo.pdf$$yPostprint 000149741 8564_ $$s1058088$$uhttps://zaguan.unizar.es/record/149741/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000149741 909CO $$ooai:zaguan.unizar.es:149741$$particulos$$pdriver 000149741 951__ $$a2025-10-17-14:09:40 000149741 980__ $$aARTICLE
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