相关论文: Partially rigid motions in the planar three-body p…

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…

Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is…

In this work, we revisit the planar restricted four-body problem to study the dynamics of an infinitesimal mass under the gravitational force produced by three heavy bodies with unequal masses, forming an equilateral triangle configuration.…

The results of our study of the motion of a three particle, self-gravitating system in general relativistic lineal gravity is presented for an arbitrary ratio of the particle masses. We derive a canonical expression for the Hamiltonian of…

We consider the problem of $n$ points with positive masses interacting pairwise with forces inversely proportional to the distance between them. In particular, it is the classical gravitational, Coulomb or photo-gravitational $n$-body…

We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the…

We consider the Newtonian planar three-body problem, defining a syzygy (velocity syzygy) as a configuration where the positions (velocities) of the three bodies become collinear. We demonstrate that if the total energy is negative, every…

The relative equilibria for the spherical, finite density 3 body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical 5 relative equilibria for the point-mass 3-body…

Recent work in the literature has studied the restricted three-body problem within the framework of effective-field-theory models of gravity. This paper extends such a program by considering the full three-body problem, when the Newtonian…

We study the acceleration and collisions of rigid bodies in special relativity. After a brief historical review, we give a physical definition of the term `rigid body' in relativistic straight line motion. We show that the definition of…

Consider the Restricted Planar Circular 3 Body Problem with both realistic mass ratio and Jacobi constant for the Sun-Jupiter pair. We prove the existence of all possible combinations of past and future final motions. In particular, we…

The planar $(n+1)$-body problem models the motion of $n+1$ bodies in the plane under their mutual Newtonian gravitational attraction forces. When $n\ge 3$, the question about final motions, that is, what are the possible limit motions in…

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…

Let a number, N, of particles interact classically through Newton's Laws of Motion and Newton's inverse square Law of Gravitation. The resulting equations of motion provide an approximate mathematical model with numerous applications in…

Continuing work initiated in earlier publications [Yamada, Asada, Phys. Rev. D 82, 104019 (2010), 83, 024040 (2011)], we investigate the post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem. For…

The simplest non-collision solutions of the N-body problem are the "relative equilibria", in which each body follows a circular orbit around the centre of mass and the shape formed by the N bodies is constant. It is easy to see that the…

Continuing work initiated in an earlier publication [Yamada, Tsuchiya, and Asada, Phys. Rev. D 91, 124016 (2015)], we reexamine the linear stability of the triangular solution in the relativistic three-body problem for general masses by the…

In the cosmos, any two bodies share a gravitational attraction. When in proximity to one another in empty space, their motions can be modeled by Newtonian gravity. Newton found their orbits when the two bodies are infinitely small, the…

It is well known that a rotation of a free generic three-dimensional rigid body is stationary if and only if it is a rotation around one of three principal axes of inertia. As it was noted by many authors, the analogous result is true for a…

The restricted planar elliptic three body problem models the motion of a massless body under the Newtonian gravitational force of the two other bodies, the primaries, which evolve in Keplerian ellipses. A trajectory is called oscillatory if…