Frequency modified fourier transform and its application to asteroids
- 184 Downloads
- 85 Citations
Abstract
Recently a method has been suggested to analyze the chaotic behaviour of a conservative dynamical system by numerical analysis of the fundamental frequencies. Frequencies and amplitudes are determined step by step. As the frequencies are not generally orthogonal, a Gramm-Schmidt orthogonalization is made and for each new frequency the old amplitudes of previously determined frequencies are corrected. For a chaotic trajectory variations of the frequencies and amplitudes determined over different time periods are expected. The change of frequencies in such a calculation is a measure of the chaoticity of the trajectory. While amplitudes are corrected, the frequencies (once determined) are constant. We suggest here simple linear corrections of frequencies for the effect of other close frequencies. The improvement of frequency determination is demonstrated on a model case. This method is applied to the first fifty numbered asteroids.
Key words
Asteroids Chaos Fourier TransformPreview
Unable to display preview. Download preview PDF.
References
- Laskar, J. 1988, ‘Secular evolution of the solar system over 10 million years’, Astron. Astrophys. 198, pp. 341–362Google Scholar
- Laskar, J.: 1990, ‘The Chaotic Motion of the Solar System: A Numerical Estimate of the Size of the Chaotic Zones’, Icarus 88, pp. 266–291Google Scholar
- Laskar, J., Froeschlé, Cl. and Celleti, A.: 1992, ‘The Measure of Chaos by the Numerical Analysis of the Fundamental Frequencies. Application to the Standard Mapping.’, Physica D 56, pp. 253–269Google Scholar
- Laskar, J.: 1993, ‘Frequency analysis for multi-dimensional systems. Global dynamics and diffusion’, Physica D 67, pp. 257–281Google Scholar
- Nesvorný, D. and Ferraz-Mello, S.: 1996, ‘Chaotic diffusion in the 2/1 asteroidal resonance’, submitted to Astron. Astrophys. Google Scholar
- Nobili, A.M., Milani, A. and Carpino, M.: 1989, ‘Fundamental frequencies and small divisors in the orbits of the outer planets’, Astron. Astrophys. 210, pp. 313–336Google Scholar
- Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P.: 1992, Numerical Recipes in C, Cambridge University Press, Cambridge, UKGoogle Scholar
- Šidlichovský, M. and Nesvorný, D.: 1994, ‘Temporary capture of grains in exterior resonances with the Earth: Planar circular restricted three-body problem with PoyntingRobertson drag’, Astron. Astrophys. 289, pp. 972–982Google Scholar