相关论文: Closed Form Approximations for the Trajectories of…
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…
A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid…
Suppose that the initial triangle formed by the three moving masses of the three-body problem is similar to the triangle formed at some later time. We derive a simple integral formula for the overall rotation relating the two triangles. The…
A simple rearrangement of the torque free motion Hamiltonian shapes it as a perturbation problem for bodies rotating close to the principal axis of maximum inertia, independently of their triaxiality. The complete reduction of the main part…
In the present paper, using the first-order approximation of the $n$-body Lagrangian (derived on the basis of the post-Newtonian gravitational theory of Einstein, Infeld, and Hoffman), we explicitly write down the equations of motion for…
The Newtonian restricted three-body problem involving a positive primary point mass, $m_+$, and a negative secondary point mass, $m_-$, in a circular orbit, and a positive or negative tertiary point mass, $m_3$, with $m_+ > |m_-| \gg…
The Lagrangian, the Hamiltonian and the constant of motion of the gravitational attraction of two bodies when one of them has variable mass is considered. This is done by choosing the reference system in one of the bodies which allows to…
This article serves as a pedagogical introduction to the problem of motion in classical field theories. The primary focus is on self-interaction: How does an object's own field affect its motion? General laws governing the self-force and…
We consider the 3-body problem in relativistic lineal gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly-bound orbits of higher frequency compared to…
In this paper,we have found the equations of motion of Generalized Photogravitational restricted three body problem with Poynting-Robertson drag. The problem is generalized in the sense that smaller primary is supposed to be an oblate…
The motion of celestial bodies in astronomy is closely related to the orbits of electrons encircling an atomic nucleus. Bohr and Sommerfeld presented a quantization scheme of the classical orbits to analyze the eigenstates of the hydrogen…
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…
We revisit the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particles move periodically in a single closed…
We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical $N$-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using…
The problem of the two-body gravitational interaction has been solved numerically based on the classical mechanics principles. One of the bodies is a deformable three-axis ellipsoid (central body) and the other is a material point…
We focus on three distinct lines of recent developments: edge modes and boundary charges in gravitational physics, relational dynamics in classical and quantum gravity, and quantum reference frames. We argue that these research directions…
In the framework of multi-body dynamics, successive encounters with a third body, even if well outside of its sphere of influence, can noticeably alter the trajectory of a spacecraft. Examples of these effects have already been exploited by…
The two body problem in a scalar theory of gravity is investigated. We focus on the closest theory to General Relativity (GR), namely Nordstr\"om's theory of gravity (1913). The gravitational field can be exactly solved for any…
The circular restricted three body problem, which considers the dynamics of an infinitesimal particle in the presence of the gravitational interaction with two massive bodies moving on circular orbits about their common center of mass, is a…
This paper aims to discuss two issues that can have a significant impact on the foundations of the theory of gravitation: (1). The existence of relativity of space-time geometry with respect to the properties of used reference frame, which…