相关论文: On shape sphere and rotation of three-body motion

We extend coupled-cluster theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of…

In Euclidean relational particle mechanics, only relative times, relative angles and relative separations are meaningful. Barbour--Bertotti (1982) theory is of this form and can be viewed as a recovery of (a portion of) Newtonian mechanics…

It is conjectured that every cusped hyperbolic 3-manifold has a decomposition into positive volume ideal hyperbolic tetrahedra (a "geometric" triangulation of the manifold). Under a mild homology assumption on the manifold we construct…

A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…

We achieve compositions rules for the geometric parameters of the composed rotations, which is in a certain sense analogous to the well known Rodrigues formula. We also obtain a necessary and sufficient condition for a composition of two…

In the traditional view, heavy deformed nuclei are like axially-symmetric prolate ellipsoids, rotating about one of the short axes. In the present picture, their shapes may be triaxial. The triaxial shape yields complex rotations, which…

We are interested in the naive problem whether we can move a solid object in a solid box or not. We restrict move to rotation. In the case we can, the centre and the ``direction'' of rotation may be restricted. Simplifying, we consider…

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…

We derive a general formula for the inertia tensor of a three-body system. By employing three independent Lagrange undetermined multipliers to express the vectors corresponding to the sides in terms of the position vectors of the vertices,…

We prove that for any knot $K$, there exists a one-vertex triangulation of the $3$-sphere containing an edge forming $K$. The proof is constructive, and based on fully augmented links. We use our method to produce ``complicated'' simplicial…

The independent eigenstates of the total orbital angular momentum operators for a three-body system in an arbitrary D-dimensional space are presented by the method of group theory. The Schr\"{o}dinger equation is reduced to the generalized…

The spontaneous motion of a camphor particle with a slight modification from a circle is investigated. The effect of the shape on the motion is examined by the perturbation method. We introduce a slight $n$-mode modification from a circle,…

An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based in calculations known from classical mechanics, but with the addition of the necessary…

We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…

In this paper we describe a procedure to simplify any given triangulation of the 3-sphere using Pachner moves. We obtain an explicit exponential-type bound on the number of Pachner moves needed for this process. This leads to a new…

We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…

The free fall of three particles under Newtonian attraction allows to illustrate some of the complexities of the general three body problem. The total collapse or singularity that occurs when starting from one of the five central…

There are periodic solutions to the equal-mass three-body (and N-body) problem in Newtonian gravity. The figure-eight solution is one of them. In this paper, we discuss its solution in the first and second post-Newtonian approximations to…

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…

This paper investigates the coplanar and circular three-body problem in the parametrized post-Newtonian (PPN) formalism, for which we focus on a class of fully conservative theories characterized by the Eddington-Robertson parameters…