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Astron. Astrophys. 351, 1149-1164 (1999)

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The 3D elliptic restricted three-body problem: periodic orbits which bifurcate from limiting restricted problems

Complex instability

Mercè Ollé and Joan R. Pacha

Dept. de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, E-08028 Barcelona, Spain (olle@ma1.upc.es; joanr@vilma.upc.es)

Received 23 April 1999 / Accepted 19 July 1999


In the present work we use certain isolated symmetric periodic orbits found in some limiting Restricted Three-Body Problems to obtain, by numerical continuation, families of symmetric periodic orbits of the more general Spatial Elliptic Restricted Three Body Problem. In particular, the Planar Isosceles Restricted Three Body Problem, the Sitnikov Problem and the MacMillan problem are considered. A stability study for the periodic orbits of the families obtained - specially focused to detect transitions to complex instability - is also made.

Key words: celestial mechanics, stellar dynamics

Send offprint requests to: Mercè Ollé

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© European Southern Observatory (ESO) 1999

Online publication: November 16, 1999