 Lindstedt–Poincaré method and periodic families of the Barbanis–Contopoulos Hamiltonian systemSaâd Benbachir Mathematics and Computers in Simulation (MATCOM), 2000, vol. 51, issue 6, 579-596 Abstract: In this work, we apply the Lindstedt–Poincaré method in order to seek the periodic solutions of the Barbanis–Contopoulos nonintegrable Hamiltonian system. We first prove that this system admits six nontrivial periodic families in the neighbourhood of the origin. Then we compute the series representing these families up to O(ϵ20A21)and their periods up to O(ϵ20A20) by means of the computer algebra system ‘Mathematica’, where A is the zeroth-order amplitude and ϵ is a perturbative parameter. We also test the validity of the LP series using a numerical integration technique. Moreover we give the periods up to O(ϵ20E10), where E is the energy, and prove that the period of the two ‘oblique’ periodic families is exactly equal to a Gauss hypergeometric series. Using the Bulirsch–Stoer algorithm we compute with good accuracy the radius of convergence of the ‘circular’ period. Finally, we compare our results with those of a ‘geometrical, method. Keywords: Lindstedt–Poincaré method; Barbanis–Contopoulos system; Periodic solutions; Symbolic computation; Acceleration of the convergence (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:51:y:2000:i:6:p:579-596 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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