Journal ArticleDOI
On the stability of the lagrangian points in the spatial restricted problem of three bodies
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In this article, the problem of stability of the Lagrangian equilibrium point of the circular restricted problem of three bodies is investigated in the light of Nekhoroshev-like theory.Abstract:
The problem of stability of the Lagrangian equilibrium point of the circular restricted problem of three bodies is investigated in the light of Nekhoroshev-like theory. Looking for stability over a time interval of the order of the estimated age of the universe, we find a physically relevant stability region. An application of the method to the Sun-Jupiter and the Earth-Moon systems is made. Moreover, we try to compare the size of our stability region with that of the region where the Trojan asteroids are actually found; the result in such case is negative, thus leaving open the problem of the stability of these asteroids.read more
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On the vertical families of two-dimensional tori near the triangular points of the bicircular problem
Enric Castellà,Àngel Jorba +1 more
TL;DR: In this article, the Lagrangian points are no longer equilibrium solutions for the bicircular problem, due to the periodic forcing coming from the Sun, and the BCP has three periodic orbits (with the same period as the forcing) that can be seen as the dynamical equivalent of the Lipschitz points.
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A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems
TL;DR: In this article, the authors present an approach based on algebraic manipulation of formal series with numerical coefficients for them, which allows big savings in memory and execution time in comparison with the use of commercial algebraic manipulators.
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The resonant structure of Jupiter's Trojan asteroids - II. What happens for different configurations of the planetary system
TL;DR: In this paper, a general method based on the knowledge of the fundamental frequencies of the planets and on those that can be reached by the Trojans is presented to predict and localize the main events arising in the swarms during migration.
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Kolmogorov and Nekhoroshev theory for the problem of three bodies
TL;DR: In this article, the authors investigated the long time stability in Nekhoroshev's sense for the Sun- Jupiter-Saturn problem in the framework of the problem of three bodies and showed that the stability for a time comparable with the age of the universe is actually reached, with some strong truncations on the perturbation expansion of the Hamiltonian at some stage.
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Numerical computation of normal forms around some periodic orbits of the restricted three-body problem
Àngel Jorba,Jordi Villanueva +1 more
TL;DR: In this paper, the authors introduce a general methodology for computing the normal form around a periodic orbit of an autonomous real analytic Hamiltonian system, which is carried out up to some finite order and, neglecting the remainder, they obtain an accurate description of the dynamics in a small enough neighborhood of the orbit.
References
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Journal ArticleDOI
An exponential estimate of the time of stability of nearly-integrable hamiltonian systems
TL;DR: The main ideas of the proof of the exponential estimate were discussed in this paper, including steepness conditions and forbidden motions of the discs of fast drift on the steepness of the unperturbed Hamiltonian.
Journal Article
Sur les courbes invariantes par les difféomorphismes de l'anneau. II
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Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem
TL;DR: In this paper, an n -degrees of freedom Hamiltonian system near an elliptic equilibrium point is considered, and the system is put in normal form (up to an arbitrary order and with respect to some resonance module) and estimates are obtained for both the size of the remainder and for the domain of convergence of the transformation leading to normal form.
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Stability of the triangular lagrangian points
TL;DR: In this paper, it was shown that the set of exceptional mass ratios for which stability remains to be proved or invalidated contains only one point besides the critical mass ratios of order two and three.