相关论文: The contact geometry of the restricted 3-body prob…

We show that a hypersurface of the regularized, spatial circular restricted three-body problem is of contact type whenever the energy level is below the first critical value (the energy level of the first Lagrange point) or if the energy…

We study the contact geometry of the connected components of the energy hypersurface, in the symmetric restricted 3-body problem on $\mathbb{S}^2$, for a specific type of motion of the primaries. In particular, we show that these components…

It is well-known that the planar and spatial circular restricted three-body problem (CR3BP) is of contact type for all energy values below the first critical value. Burgos-Garc\'ia and Gidea extended Hill's approach in the CR3BP to the…

We introduce a circular restricted charged three-body problem on the plane. In this model, the gravitational and Coulomb forces, due to the primary bodies, act on a test particle; the net force exerted by some primary body on the test…

In this paper, we study the planar circular restricted three-body problem for energy levels slightly above the first critical value. We first observe that the energy hypersurfaces in the Birkhoff regularization corresponding to these energy…

We show in this work that the restricted three-body problem is in general not of contact type and zero is the energy value where the contact property breaks down. More explicitly, sequences of generating orbits with increasingly negative…

The case of the planar circular restricted three-body problem is used as a test field in order to determine the character of the orbits of a small body which moves under the gravitational influence of the two heavy primary bodies. We…

The elliptic restricted three body problem has been well studied. However, the previous formulations of the problem have used a rotating coordinate system to keep the positions of the primary and secondary on the x-axis. This requires the…

The two and three-body contacts are central to a set of univeral relations between microscopic few-body physics within an ultracold Bose gas and its thermodynamical properties. They may also be defined in trapped few-particle systems, which…

In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…

A book, concerning the classical restricted three body problem, and the approach to this old conundrum coming from the modern methods of symplectic and contact geometry. It is split into Part I (theoretical aspects), and Part II (practical…

In the restricted three-body problem, consecutive collision orbits are those orbits which start and end at collisions with one of the primaries. Interests for such orbits arise not only from mathematics but also from various engineering…

An approach is developed to find approximate solutions to the restricted circular three body problem. The solution is useful in approximately describing the position vectors of three spherically symmetric masses, one of which has a much…

In this paper we classify the central configurations of the circular restricted 4-body problem with three primaries at the collinear configuration of the 3-body problem and an infinitesimal mass. The case where the three primaries have the…

The restricted planar three-body problem has a rich history, yet many unanswered questions still remain. In the present paper we prove the existence of a global surface of section near the smaller body in a new range of energies and mass…

General properties of the three-body problem in a model of modified dynamics are investigated. It is shown that the three-body problem in this model shares some characters with the similar problem in Newtonian dynamics. Moreover, the planar…

The case of the planar circular restricted three-body problem where one of the two primaries has a stronger gravitational field with respect to the classical Newtonian field is investigated. We consider the case where two primaries have the…

We establish a general criterion for the existence of finite energy foliations on contact three-manifolds with boundary, imposing strong global constraints on the associated Reeb flows. Our main abstract result shows that a configuration of…

We investigate the planar Dirac equation with the most general time-independent contact (singular) potential supported on a circumference. Taking advantage of the radial symmetry, the problem is effectively reduced to a one-dimensional one…

The restricted three body problem is well-known and very important for dynamics of binary, multiple stars and also planetary systems. We extend the classical version of this problem to the situation that there are some external forces from…