Zobrazeno 1 - 10
of 530
pro vyhledávání: '"Chavela, A."'
We investigate the relationship between rigid motions and relative equilibria in the N-body problem on the two-dimensional sphere, S2. We prove that any rigid motion of the N-body system on S2 must be a relative equilibrium. Our approach extends the
Externí odkaz:
http://arxiv.org/abs/2409.16545
We study orbits near collision in a non-autonomous restricted planar four-body problem. This restricted problem consists of a massless particle moving under the gravitational influence due to three bodies following the figure-eight choreography. We u
Externí odkaz:
http://arxiv.org/abs/2404.01463
In the planar three-body problem under Newtonian potential, it is well known that any masses, located at the vertices of an equilateral triangle generates a relative equilibrium, known as the Lagrange relative equilibrium. In fact, the equilateral tr
Externí odkaz:
http://arxiv.org/abs/2311.02770
We study relative equilibria ($RE$ in short) for three-body problem on $\mathbb{S}^2$, under the influence of a general potential which only depends on $\cos\sigma_{ij}$ where $\sigma_{ij}$ are the mutual angles among the masses. Explicit conditions
Externí odkaz:
http://arxiv.org/abs/2309.06603
The positive curved three body problem is a natural extension of the planar Newtonian three body problem to the sphere $\mathbb{S}^2$. In this paper we study the extensions of the Euler and Lagrange Relative equilibria ($RE$ in short) on the plane to
Externí odkaz:
http://arxiv.org/abs/2306.13838
We develop a new geometrical technique to study relative equilibria for a system of $n$--positive masses, moving on the two dimensional sphere $\mathbb{S}^2$, under the influence of a general potential which only depends on the mutual distances among
Externí odkaz:
http://arxiv.org/abs/2304.13782
Relative equilibria on a rotating meridian on $\mathbb{S}^2$ in equal-mass three-body problem under the cotangent potential are determined. We show the existence of scalene and isosceles relative equilibria. Almost all isosceles triangles, including
Externí odkaz:
http://arxiv.org/abs/2203.14930
This is a natural continuation of our first paper \cite{pre}, where we develop a new geometrical technique which allow us to study relative equilibria on the two sphere. We consider a system of three positive masses on $\mathbb{S}^2$ moving under the
Externí odkaz:
http://arxiv.org/abs/2202.12708
Using the properties of the angular momentum, we develop a new geometrical technique to study relative equilibria for a system of $3$--bodies with positive masses, moving on the two sphere under the influence of an attractive potential depending only
Externí odkaz:
http://arxiv.org/abs/2202.10351
We consider autonomous Newtonian systems with Coriolis forces in two and three dimensions and study the existence of branches of periodic orbits emanating from equilibria. We investigate both degenerate and nondegenerate situations. While Lyapunov's
Externí odkaz:
http://arxiv.org/abs/2108.13312