2017/01/17 by Euaggelos E. Zotos · 4 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Applied mathematics #Classical mechanics #Computer science #Convergence (economics) #Geomagnetism and Paleomagnetism Studies #Lagrangian point #Mathematical analysis #Mathematics #Newton's method #Nonlinear system #Physics #Position (finance) #Scientific Research and Discoveries #Stability (learning theory) #Theoretical and Computational Physics #nlin.CD
paper · pdf · doi:10.1016/j.ijnonlinmec.2017.01.009
published as IJNLM, vol. 90, 111-123 (2017) · Published in International Journal of Non-Linear Mechanics (IJNLM). arXiv admin note: previous papers with related context: arXiv:1702.07279, arXiv:1608.08610
openalex publication_date 2017/01/17 · openalex created_date 2017/01/26 · arxiv created 2017/09/21 · arxiv updated 2017/09/28 · openalex updated_date 2026/08/05
The Copenhagen problem where the primaries of equal masses are magnetic dipoles is used in order to determine the Newton-Raphson basins of attraction associated with the equilibrium points. The parametric variation of the position as well as of the stability of the Lagrange points are monitored when the value of the ratio λ of the magnetic moments varies in predefined intervals. The regions on the configuration (x,y) plane occupied by the basins of convergence are revealed using the multivariate version of the Newton-Raphson iterative scheme. The correlations between the basins of attraction of the libration points and the corresponding number of iterations needed for obtaining the desired accuracy are also illustrated. We perform a thorough and systematic numerical investigation by demonstrating how the dynamical quantity λ influences the shape, the geometry and also the degree of fractality of the attracting domains. Our numerical results strongly indicate that the ratio λ is indeed a very influential parameter in the electromagnetic binary system.