Open AccessOrbit classification in arbitrary 2D and 3D potentials
Author(s) -
Carpintero Daniel D.,
Aguilar Luis A.
Publication year - 1998
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.1998.01320.x
Subject(s) - physics , fortran , orbit (dynamics) , code (set theory) , orientation (vector space) , principal axis theorem , position (finance) , algorithm , rank (graph theory) , character (mathematics) , coordinate system , fourier transform , principal component analysis , mathematical analysis , geometry , computer science , artificial intelligence , combinatorics , mathematics , engineering , aerospace engineering , set (abstract data type) , finance , quantum mechanics , economics , programming language , operating system
A method of classifying generic orbits in arbitrary 2D and 3D potentials is presented. It is based on the concept of spectral dynamics introduced by Binney &38; Spergel that uses the Fourier transform of the time series of each coordinate. The method is tested using a number of potentials previously studied in the literature and is shown to distinguish correctly between regular and irregular orbits, to identify the various families of regular orbits (boxes, loops, tubes, boxlets, etc.), and to recognize the second‐rank resonances that bifurcate from them. The method returns the position of the potential centre and, for 2D potentials, the orientation of the principal axes as well, should this be unknown. A further advantage of the method is that it has been encoded in a FORTRAN program that does not require user intervention, except for ‘fine tuning’ of search parameters that define the numerical limits of the code. The automatic character makes the program suitable for classifying large numbers of orbits.