Frequency modified Fourier transform and its application to asteroids (Q1364250)

The authors propose a modification of the recursive algorithm for the modified Fourier transform (MFT). As is well-known for regular motion, MFT yields an analytical representation of the solutions, while for chaotic systems the frequency changes calculated for two time intervals give a measure of chaos (chaoticity of the trajectory). The modification proposed consists in linear corrections of frequencies for the effect of the other close frequencies, and is demonstrated on a model case. The frequency MFT is also applied to the first fifty numbered asteroids, and numerical results are given.