We investigate the dynamics associated to nearly integrable dissipative systems, with particular reference to some models of Celestial Mechanics which can be described in a weakly dissipative framework. We start by studying some paradigmatic models provided by the dissipative standard maps in two- and four-dimensions. The dynamical investigation is performed applying frequency analysis and computing the differential fast Lyapunov indicators. After recalling a few properties of adiabatic invariants, we provide some examples of nearly integrable dissipative systems borrowed from Celestial Mechanics, and precisely the spin-orbit coupling and the three-body problem. We conclude with a discussion on the existence of periodic orbits in dissipative autonomous and non-autonomous systems. © 2007 Springer-Verlag Berlin Heidelberg.

Celletti, A. (2007). Weakly dissipative systems in celestial mechanics, 729, 67-90 [10.1007/978-3-540-72984-6_3].

Weakly dissipative systems in celestial mechanics

CELLETTI, ALESSANDRA
2007-01-01

Abstract

We investigate the dynamics associated to nearly integrable dissipative systems, with particular reference to some models of Celestial Mechanics which can be described in a weakly dissipative framework. We start by studying some paradigmatic models provided by the dissipative standard maps in two- and four-dimensions. The dynamical investigation is performed applying frequency analysis and computing the differential fast Lyapunov indicators. After recalling a few properties of adiabatic invariants, we provide some examples of nearly integrable dissipative systems borrowed from Celestial Mechanics, and precisely the spin-orbit coupling and the three-body problem. We conclude with a discussion on the existence of periodic orbits in dissipative autonomous and non-autonomous systems. © 2007 Springer-Verlag Berlin Heidelberg.
2007
Pubblicato
Rilevanza internazionale
Capitolo o saggio
Nessuno
Settore MAT/07 - FISICA MATEMATICA
English
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Celletti, A. (2007). Weakly dissipative systems in celestial mechanics, 729, 67-90 [10.1007/978-3-540-72984-6_3].
Celletti, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/27109
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