By Andrea Milani, Zoran Knežević (auth.), Rudolf Dvorak, Sylvio Ferraz-Mello (eds.)
The papers during this quantity conceal quite a lot of matters overlaying the newest advancements in Celestial Mechanics from the theoretical aspect of nonlinear dynamical structures to the applying to actual difficulties. We emphasize the papers at the formation of planetary structures, their balance and in addition the matter of liveable zones in extrasolar planetary structures. a different subject is the steadiness of Trojans in our planetary procedure, the place an increasing number of real looking dynamical types are used to provide an explanation for their complicated motions: along with the $64000 contribution from the theoretical perspective, the result of numerous numerical experiments unraveled the constitution of the solid area round the librations issues.
This quantity could be of curiosity to astronomers and mathematicians attracted to Hamiltonian mechanics and within the dynamics of planetary systems.
Read or Download A Comparison of the Dynamical Evolution of Planetary Systems: Proceedings of the Sixth Alexander von Humboldt Colloquium on Celestial Mechanics Bad Hofgastein (Austria), 21–27 March 2004 PDF
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Extra resources for A Comparison of the Dynamical Evolution of Planetary Systems: Proceedings of the Sixth Alexander von Humboldt Colloquium on Celestial Mechanics Bad Hofgastein (Austria), 21–27 March 2004
A correction factor to this result is estimated as 1:28, giving Dp ’ 13:5 . Section 4 contains the main conclusions of the present study and suggestions for future research. 34 CHRISTOS EFTHYMIOPOULOS 2. 1. FORMAL INTEGRALS FOR MAPPINGS. THE DIRECT METHOD We shall consider ﬁrst the construction of formal integrals in non-linear symplectic mappings by a method, which is the discrete analog of the direct method of Whittaker (1916), Cherry (1924) and Contopoulos (1960). The method is easily exempliﬁed in the case of 2D symplectic mappings.
However, the averaging process ignores all the resonant phenomena producing chaos near the separatrix. To reintroduce these phenomena, Sa´ndor et al. (2002) used the averaged Hamiltonian hHi to produce a mapping for the Trojan motion, based on the method of Hadjidemetriou (1991). The mapping of Sa´ndor et al. reproduces the characteristics of the Poincare´ surface of section of the original Hamiltonian. In particular, the mapping has the same ﬁxed points and with the same stability as the Hamiltonian.
2005, ‘Formal integrals and Nekhoroshev stability in a mapping model for the Trojan asteroids, Celest. Mech. Dynam. Astron. 92, 31–54. : 1988, ‘Long periodic pertubations of Trojan asteroids’, Celest. Mech. Dynam. Astron. 43, 303–308. : 1997, ‘The Trojan Problem’, Celest. Mech. Dynam. Astron. 65, 149–164. : 1984, ‘The Lyapunov characteristic exponents – applications to celestial mechanics’, Celest. Mech. 34, 95. Hanslmeier, A. : 1984, ‘Numerical Integrations with Lie-series to celestial mechanics’, A&A 132, 203.