Symplectic Mapping for Trojan-Type Motion in the Elliptic Restricted Three-Body Problem

Authors: Sándor Z.¹; Érdi B.¹

Source: Celestial Mechanics and Dynamical Astronomy, Volume 86, Number 4, August 2003 , pp. 301-319(19)

Publisher: Springer

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Abstract:

A symplectic mapping for Trojan-type motion has been developed in the secularly changing elliptic restricted three-body problem. The mapping describes well the characteristics of Trojan-type dynamics at small eccentricities. By using this mapping the boundary of the stability region has been studied for different values of the initial eccentricities of hypothetical Jupiter’s Trojans. It has been found that in the secularly changing elliptic case the chaotic diffusion at the border of the stability region is stronger than simply in the elliptic case. An explanation of this observation might be the destruction of the chain of islands of the 13:1 secondary resonance between the short and long period component of the Trojan-like motion, caused possibly by the indirect perturbations of Saturn.

Keywords: symplectic mappings; elliptic restricted three-body problem; 1:1 resonance; Trojan-type motion

Language: English

Document Type: Research article

Affiliations: 1: Department of Astronomy, Eötvös University, Pázmány Péter st. 1/A, H-1117 Budapest, Hungary

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