منابع مشابه
On the Families of Periodic Orbits of the Sitnikov Problem
The main goal of this paper is to study analytically the families of symmetric periodic orbits of the elliptic Sitnikov problem for all values of the eccentricity in the interval [0, 1). The basic tool for proving our results is the global continuation method of the zeros of a function depending on one–parameter provided by Leray and Schauder and based in the Brouwer degree.
متن کاملPeriodic orbits of the Sitnikov problem via a Poincaré map
In this paper by means of a Poincaré map, we prove the existence of symmetric periodic orbits of the elliptic Sitnikov problem. Furthermore, using the presence of the Bernoulli shift as a subsystem of that Poincaré map, we prove that not all the periodic orbits of the Sitnikov problem are symmetric periodic orbits.
متن کاملChaos in Simple Dynamical Systems – the Sitnikov Problem
It is well known that in low degrees of freedom dynamical systems chaotic behaviour appears. To examine this phenomenon the Sitnikov problem is a very good example which is a special case of the restricted three-body problem. In this paper we investigate the changing of the phase space structure due to the variation of the Surfaces of Sections.
متن کاملMatched Asymptotic Expansions to the Circular Sitnikov Problem with Long Period
The circular Sitnikov problem is revisited, using matched asymptotic expansions. In the case of large oscillation periods, approximate analytical expressions for the period and the orbit of the third body are found. The results are compared with those described in the literature and show that the movement of the third body can be well described by two analytical solutions, the inner and outer s...
متن کاملGlobal bifurcations from the center of mass in the Sitnikov problem
The Sitnikov problem is a restricted three body problem where the eccentricity of the primaries acts as a parameter. We find families of symmetric periodic solutions bifurcating from the equilibrium at the center of mass.
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2014
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.11096