Global Instability in the Restricted Planar Elliptic Three Body Problem
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-018-3248-z
Abstract: The restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet or an asteroid) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter)… read more here.
Keywords: restricted planar; elliptic three; planar elliptic; body problem ... See more keywords
Oscillating about coplanarity in the 4 body problem
Sign Up to like & getrecommendations! Published in 2019 at "Inventiones mathematicae"
DOI: 10.1007/s00222-019-00879-0
Abstract: For the Newtonian 4-body problem in space we prove that any zero angular momentum bounded solution suffers infinitely many coplanar instants, that is, times at which all 4 bodies lie in the same plane. This… read more here.
Keywords: oscillating coplanarity; space; coplanarity body; body problem ... See more keywords
Perihelion Librations in the Secular Three-Body Problem
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Nonlinear Science"
DOI: 10.1007/s00332-020-09624-x
Abstract: A normal form theory for non-quasiperiodic systems is combined with the special properties of the partially averaged Newtonian potential pointed out in Pinzari (Celest Mech Dyn Astron 131(5):22, 2019) to prove, in the averaged, planar… read more here.
Keywords: perihelion librations; three body; body problem; body ... See more keywords
BiElliptic Restricted Four Body Problem
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DOI: 10.1007/s00601-018-1472-x
Abstract: The motion of an infinitesimal mass in the restricted four body problem is studied assuming both the orbits of motion of the three primaries to be elliptical. It is assumed that the forces governing the… read more here.
Keywords: restricted four; motion; four body; body problem ... See more keywords
On the perturbed photogravitational restricted five-body problem: the analysis of fractal basins of convergence
Sign Up to like & getrecommendations! Published in 2019 at "Astrophysics and Space Science"
DOI: 10.1007/s10509-019-3575-3
Abstract: In the framework of photogravitational version of the restricted five-body problem, the existence and stability of the in-plane equilibrium points, the possible regions for motion are explored and analysed numerically, under the combined effect of… read more here.
Keywords: five body; basins convergence; body problem; restricted five ... See more keywords
The transfers from lunar DROs to Earth orbits via optimization in the four body problem
Sign Up to like & getrecommendations! Published in 2021 at "Astrophysics and Space Science"
DOI: 10.1007/s10509-021-03955-1
Abstract: The distant retrograde orbits (DROs) can serve as the parking orbits for a long-term cis-lunar space station. This paper gives a comprehensive study on the transfer problem from DROs to Earth orbits, including low Earth… read more here.
Keywords: body problem; earth orbits; dros earth; four body ... See more keywords
Numerical study of the geometry of the phase space of the Augmented Hill Three-Body problem
Sign Up to like & getrecommendations! Published in 2017 at "Celestial Mechanics and Dynamical Astronomy"
DOI: 10.1007/s10569-017-9762-z
Abstract: The Augmented Hill Three-Body problem is an extension of the classical Hill problem that, among other applications, has been used to model the motion of a solar sail around an asteroid. This model is a… read more here.
Keywords: geometry; hill three; augmented hill; body problem ... See more keywords
Reduction and relative equilibria for the two-body problem on spaces of constant curvature
Sign Up to like & getrecommendations! Published in 2018 at "Celestial Mechanics and Dynamical Astronomy"
DOI: 10.1007/s10569-018-9835-7
Abstract: We consider the two-body problem on surfaces of constant nonzero curvature and classify the relative equilibria and their stability. On the hyperbolic plane, for each $$q>0$$q>0 we show there are two relative equilibria where the… read more here.
Keywords: equilibria; relative equilibria; two body; body problem ... See more keywords
The restricted three-body problem in cylindrical clouds
Sign Up to like & getrecommendations! Published in 2018 at "Celestial Mechanics and Dynamical Astronomy"
DOI: 10.1007/s10569-018-9869-x
Abstract: The fragmentation of interstellar molecular clouds has been investigated with great effort by many authors. In this paper, a simple model is given to describe the dynamics of two fragments moving in a special cylindrical… read more here.
Keywords: body problem; clouds; restricted three; three body ... See more keywords
Central configurations in the spatial n-body problem for $$n=5,6$$ with equal masses
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DOI: 10.1007/s10569-020-09993-1
Abstract: We present a computer assisted proof of the full listing of central configurations for spatial n-body problem for $$n=5$$ and 6, with equal masses. For each central configuration, we give a full list of its… read more here.
Keywords: body problem; problem equal; configurations spatial; spatial body ... See more keywords
Regularization of the Circular Restricted Three Body Problem on Surfaces of Constant Curvature
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-017-9619-x
Abstract: We consider a restricted three body problem on surfaces of constant curvature. As in the classical Newtonian case the collision singularities occur when the position particle with infinitesimal mass coincides with the position of one… read more here.
Keywords: problem surfaces; restricted three; surfaces constant; body problem ... See more keywords