Abstract
We present some examples of dynamical problems in the solar system with strong physical implications and for which regular and chaotic behaviours are fundamental.
Due to their relatively small size, asteroids are mostly primordial (i.e. they have not been affected by geological processes) and therefore can give us essential information on the physical properties of the primitive matter in the solar system. Among asteroids, those belonging to the so called families (i.e. fragments of a parent body, with low enough ejection velocities to produce initially swarms of objects having similar orbital elements) give us a unique opportunity to get information about the interior of asteroidal bodies. The problem has two faces. First to obtain, under the assumption of quasi regularity, quasi first uniform integrals of the motion: the so called proper elements, and second, to use objective statistical methods of cluster analysis. Recently, decisive improvements came from the application of high-order perturbation theories in computing the proper elements (Williams, Yuasa, Knežević and Milani) and from the use of reliable cluster analysis methods (Zappalà et al. 1990, Bendjoya et al. 1991).
On the other hand, chaotic routes are essential to bring either asteroidal material or comets in the vicinity of Earth. In order to study the chaotic behaviour of asteroidal and cometary orbits, modelling becomes an aim and a tool. Monte Carlo mappings and Markov processes are the main tools which will be discussed in this paper as well as the strength and weakness of these methods versus the origin of chaos.
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Froeschlé, C., Bendjoya, P., Cellino, A. (1994). From Integrability to Chaos: Examples of Interrelations between Physics and Dynamics for Minor Bodies in the Solar System. In: Seimenis, J. (eds) Hamiltonian Mechanics. NATO ASI Series, vol 331. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0964-0_6
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