Abstract
To investigate non-linear dynamical systems, like for instance artificial satellites, Solar System, exoplanets or galactic models, it is necessary to have at hand several tools, such as a reliable dynamical indicator.The aim of the present work is to test a relatively new fast indicator, the Mean Exponential Growth factor of Nearby Orbits (MEGNO), since it is becoming a widespread technique for the study of Hamiltonian systems, particularly in the field of dynamical astronomy and astrodynamics, as well as molecular dynamics.In order to perform this test we make a detailed numerical and statistical study of a sample of orbits in a triaxial galactic system, whose dynamics was investigated by means of the computation of the Finite Time Lyapunov Characteristic Numbers (FT-LCNs) by other authors.
Highlights
In the present work we accomplish an exhaustive study of the Mean Exponential Growth factor of Nearby Orbits (MEGNO) when applied to a given sample of orbits in a triaxial galactic potential studied by [1]
The chaotic component Oc appointed by the Finite Time Lyapunov Characteristic Numbers (FT–Lyapunov Characteristic Number (LCN)) is reattained by means of the MEGNO, i.e. all orbits in Oc have MEGNO values lying on the MEGNO irregularity range
Results at large integration times In the present section we will be concerned with the temporal evolution of the three indicators to be compared, namely the MEGNO, the LCN and the mean Fast Lyapunov Indicator (FLI) (for which no re-normalization was performed and in the case of the exponential growth of δ(t) the integration was stopped at δ(t) = 1020), for large motion times
Summary
In the present work we accomplish an exhaustive study of the MEGNO when applied to a given sample of orbits in a triaxial galactic potential studied by [1]. The MEGNO is introduced by [3] and, in [4], this technique is formalized and its application extended to discrete Hamiltonian systems like maps; a generalization of the MEGNO is introduced therein This tool has become of widespread use for studying several astronomical problems as well as many other Hamiltonian systems (see, e.g., [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]). A far more complex non–linear system is addressed that reproduces many characteristics of real elliptical galaxies, namely, the one introduced by [1] This model will be used as the scenario for a detailed comparison between the MEGNO and the Lyapunov Characteristic Numbers and even the Fast Lyapunov Indicator (FLI) introduced by [20]
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