Fast Detection of Chaotic Or Regular Behavior of Double Pendulum System: Application of the Fast Norm Vector Indicator Method

Abstract eng:
It is well known that for non-linear Hamiltonian systems there exist ordered regions with quasi-periodic orbits and regions with chaotic orbits. Usually, these regions are distributed in the phase space in very complicated ways, which often makes it very difficult to distinguish between them, especially when we are dealing with many degrees of freedom. Recently, a new, very fast and easy to compute indicator of the chaotic or ordered nature of orbits has been introduced by Zotos (2012), the so-called "Fast Norm Vector Indicator (FNVI)". Using the double pendulum system, in the paper we present a detailed numerical study comporting the advantages and the drawbacks of the FNVI to those of the Smaller Alignment Index (SALI), a reliable indicator of chaos and order in Hamiltonian systems. Our effort was focused both on the traditional behavior of the FNVI for regular and fully developed chaos but on the "sticky" orbits and on the quantitative criterion proposed by Zotos, too.

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