[ספר][B] Celestial encounters: the origins of chaos and stability
Celestial Encounters is for anyone who has ever wondered about the foundations of chaos.
In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of …
In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of …
Some problems on the classical n-body problem
A Albouy, HE Cabral, AA Santos - Celestial Mechanics and Dynamical …, 2012 - Springer
Our idea is to imitate Smale's list of problems, in a restricted domain of mathematical aspects
of Celestial Mechanics. All the problems are on the n-body problem, some with different …
of Celestial Mechanics. All the problems are on the n-body problem, some with different …
Out-of-plane dynamics: a study within the circular restricted eight-body framework
This manuscript thoroughly explores the dynamics of a test particle around out-of-plane
equilibrium points within the circular restricted eight-body problem. This particular scenario …
equilibrium points within the circular restricted eight-body problem. This particular scenario …
Central configurations of the planar coorbitalsatellite problem
We study the planar central configurations of the 1+ n body problem where one mass is
large and the other n masses are infinitesimal and equal. We find analytically all these …
large and the other n masses are infinitesimal and equal. We find analytically all these …
On the planar central configurations of the 4-body problem with three equal masses
Taking conveniently the unity of mass we can assume that three masses are equal to 1, and
the fourth one is m. First, we prove that if a central configuration has an axis of symmetry …
the fourth one is m. First, we prove that if a central configuration has an axis of symmetry …
On the central configurations of the planar 1+ 3 body problem
We consider the Newtonian four-body problem in the plane with a dominat mass M. We
study the planar central configurations of this problem when the remaining masses are …
study the planar central configurations of this problem when the remaining masses are …
Bifurcation of relative equilibria of the (1+ 3)-body problem
We study the relative equilibria of the limit case of the planar Newtonian 4-body problem
when three masses tend to zero, the so-called (1+ 3)-body problem. Depending on the …
when three masses tend to zero, the so-called (1+ 3)-body problem. Depending on the …
The vortex dynamics analogue of the restricted three-body problem: advection in the field of three identical point vortices
The passive advection of tracers in the field of three identical point vortices is considered as
the hydrodynamical analogue of the restricted three-body problem. The chaotic motion is …
the hydrodynamical analogue of the restricted three-body problem. The chaotic motion is …
Periodic orbits of discrete and continuous dynamical systems via Poincar\'{e}-Miranda theorem
We present a systematic methodology to determine and locate analytically isolated periodic
points of discrete and continuous dynamical systems with algebraic nature. We apply this …
points of discrete and continuous dynamical systems with algebraic nature. We apply this …
On Maxwell's (n+ 1)-body problem in the Manev-type field and on the associated restricted problem
V Mioc, M Stavinschi - Physica Scripta, 1999 - iopscience.iop.org
Abstract The planar symmetrical (n+ 1)-body problem in a Manev-type field (featured by a
potential of the form α/r+ β/r 2) is being tackled. One proves that, if n equal masses are …
potential of the form α/r+ β/r 2) is being tackled. One proves that, if n equal masses are …