Read e-book online A Comparison of the Dynamical Evolution of Planetary PDF

By Andrea Milani, Zoran Knežević (auth.), Rudolf Dvorak, Sylvio Ferraz-Mello (eds.)

ISBN-10: 1402042183

ISBN-13: 9781402042188

ISBN-10: 1402044666

ISBN-13: 9781402044663

The papers during this quantity hide quite a lot of matters masking the latest advancements in Celestial Mechanics from the theoretical element of nonlinear dynamical structures to the applying to genuine difficulties. We emphasize the papers at the formation of planetary platforms, their balance and likewise the matter of liveable zones in extrasolar planetary structures. a different subject is the steadiness of Trojans in our planetary method, the place increasingly more real looking dynamical versions are used to give an explanation for their complicated motions: in addition to the real contribution from the theoretical perspective, the result of a number of numerical experiments unraveled the constitution of the reliable region round the librations issues.
This quantity might be of curiosity to astronomers and mathematicians drawn to Hamiltonian mechanics and within the dynamics of planetary systems.

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Read Online 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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Additional info 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

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Are complex polynomial functions of order s in the variables ðz; zà Þ. Furthermore, if the mapping equations (12) are truncated at order N, the symplecticity condition is satisfied also up to terms of order N. The linearized map z0 ¼ eix z possesses the exact integral ð13Þ U2 ðz; zÃ Þ ¼ zzà ; which represents circles around the origin. We look for a formal integral of the non-linear mapping (12) starting with the term (13), namely Uðz; zÃ Þ ¼ U2 ðz; zÃ Þ þ U3 ðz; zÃ Þ þ Á Á Á ¼ zzà þ a30 z3 þ a21 z2 zà þ a12 zz2à þ a03 z3à þ Á Á Á ¼ 1 X ð14Þ apq zp zqà : p;qP0;pþq¼2 For p þ q ¼ 2 we have apq ¼ dpq .

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Beauge´, C. : 2001, Icarus 153, 391. , Galgani, L. : 1985, Cel. Mech. 37, 1. Birkhoff, G. : 1920, Acta Math. 43, 1. Celletti, A. : 1991, Cel. Mech. Dyn. Astr. 50, 31. , Giorgilli, A. : 2000, Non-linearity 13, 397. Cherry, T. : 1924, Proc. Cambridge Phil. Soc. 22, 325, 510. : 1963, Astron. J. 68, 763. : 1960, Z. Astroph. 49, 273. Dvorak, R. : (2000), Cel. Mech. Dyn. Astr. 78, 125. , Giorgilli, A. : 2004, J. Phys. A 37, 10831–10858. : 1988, Cel. Mech. 43, 303. : 1997, Cel. Mech. Dyn. Astr. 65, 149.

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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 by Andrea Milani, Zoran Knežević (auth.), Rudolf Dvorak, Sylvio Ferraz-Mello (eds.)


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