A review on Poincaré research in celestial mechanics and dynamics (stable and unstable periodic motions)

H. Poincaré considers in his Méthodes Nouvelles the asymptotic solutions obtained as particular solutions of Bohlin planetary perturbation method. He shows that several periodic solutions may appear when special invariant relationships are stated as initial conditions of this problem. The main resul...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autor principal: Altavista, Carlos Alberto
Formato: Articulo Comunicacion
Lenguaje:Español
Publicado: 1993
Materias:
Astronomía
Galaxia
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/148682
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-148682
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Español
topic Astronomía
Galaxia
spellingShingle Astronomía
Galaxia
Altavista, Carlos Alberto
A review on Poincaré research in celestial mechanics and dynamics (stable and unstable periodic motions)
topic_facet Astronomía
Galaxia
description H. Poincaré considers in his Méthodes Nouvelles the asymptotic solutions obtained as particular solutions of Bohlin planetary perturbation method. He shows that several periodic solutions may appear when special invariant relationships are stated as initial conditions of this problem. The main results can be summarized as follows: I) Real (true) periodic solutions arise when the stated invariant relationships are equivalent to the conditions stated for obtaining periodic solutions of the first sort. These solutions are, then convergent (stable). II) If the initial conditions are different from the previous ones, periodic solutions can also be obtained. But, in this case, they are unstable. The essential difference between both cases rest upon the way in which the mean motions of masses are combined. Periodic solutions may also be obtained by applying the fixed point theorem. In fact, it may be shown that Riccati's equations in the complex domain can be used as perturbation equations. The dependent variables are the quantities p, q, r ( the instantaneous rotations of orbital system of coordinates, referred with respect to a fixed frame). These equations remain invariable under a bilinear transformations (Möbius). Since Möbius transformations may have a fixed stable point, the transformation theory shows that complete stability takes place in case of linear approximation. Then complete stability remains valid for the non-linear approximation, and the existence of a fixed point in the solutions is assured. Then, periodic orbits exist under such circumstances.
format Articulo
Comunicacion
author Altavista, Carlos Alberto
author_facet Altavista, Carlos Alberto
author_sort Altavista, Carlos Alberto
title A review on Poincaré research in celestial mechanics and dynamics (stable and unstable periodic motions)
title_short A review on Poincaré research in celestial mechanics and dynamics (stable and unstable periodic motions)
title_full A review on Poincaré research in celestial mechanics and dynamics (stable and unstable periodic motions)
title_fullStr A review on Poincaré research in celestial mechanics and dynamics (stable and unstable periodic motions)
title_full_unstemmed A review on Poincaré research in celestial mechanics and dynamics (stable and unstable periodic motions)
title_sort review on poincaré research in celestial mechanics and dynamics (stable and unstable periodic motions)
publishDate 1993
url http://sedici.unlp.edu.ar/handle/10915/148682
work_keys_str_mv AT altavistacarlosalberto areviewonpoincareresearchincelestialmechanicsanddynamicsstableandunstableperiodicmotions
AT altavistacarlosalberto reviewonpoincareresearchincelestialmechanicsanddynamicsstableandunstableperiodicmotions
bdutipo_str Repositorios
_version_ 1764820461651230721

Ejemplares similares