Related papers: "Twist Vectors" for Central Configuration Equation…
Various many-body models are treated, which describe $N$ points confined to move on a plane circle. Their Newtonian equations of motion ("accelerations equal forces") are integrable, i. e. they allow the explicit exhibition of $N$ constants…
We have numerically computed planar central configurations of $n=1000$ bodies of equal masses. A classification of central configurations is proposed based on the numerical value of the complexity, $\mathcal{C}$. The main result of our work…
Nonlinear N-body integrable Hamiltonian systems, where N is an arbitrary number, attract the attention of mathematical physicists for the last several decades, following the discovery of some number of these systems. This paper presents a…
I consider a self-gravitating, N-body system assuming that the N constituents follow regular orbits about the center of mass of the cluster, where a central massive object may be present. I calculate the average over a characteristic…
Recent advances in curved N=2 superspace methods have rendered the component reduction of superspace actions more feasible than in the past. In this paper, we consider models involving both vector and tensor multiplets coupled to…
In this work, we seek a cosmological mechanism that may define the sign of the effective gravitational coupling constant, {\em G}. To this end, we consider general scalar-tensor gravity theories as they provide the field theory natural…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
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…
For the planar four-vortex problem, we show that there are finitely many stationary configurations consisting of equilibria, rigidly translating configurations, relative equilibria (uniformly rotating configurations) and collapse…
For the power-law potential $n$-body problem, we study a special kind of central configurations where all the masses lie on a circle and the center of mass coincides with the center of the circle. It is also called the centered co-circular…
We study central configurations of the Newtonian four-body problem that form a trapezoid. Using a topological argument we prove that there is at most one trapezoidal central configuration for each cyclic ordering of the masses.
We investigate the n-body problem on a sphere with a general interaction potential that depends on the mutual distances. We focus on the equilibrium configurations, especially on the Dziobek equilibrium configurations, which is an analogy…
One of the oldest problems in physics is that of calculating the motion of $N$ particles under a specified mutual force: the $N$-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and…
A conceptual framework for variational formulations of physical theories is proposed. Such a framework is displayed here just for statics, but it is designed to be subsequently adapted to variational formulations of static field theories…
We prove that all non-degenerate relative equilibria of the planar Newtonian $n$--body problem can be continued to spaces of constant curvature $\kappa$, positive or negative, for small enough values of this parameter. We also compute the…
Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A…
We consider spherically symmetric higher-dimensional solutions of Einstein's equations with a bulk cosmological constant and n transverse dimensions. In contrast to the case of one or two extra dimensions we find no solutions that localize…
This paper introduces a new difference scheme to the difference equations for N-body type problems. To find the non-collision periodic solutions and generalized periodic solutions in multi-radial symmetric constraint for the N-body type…
We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…
This article studies the N-vortex problem in the plane with positive vorticities. After an investigation of some properties for normalised relative equilibria of the system, we use symplectic capacity theory to show that, there exist…