Related papers: Relative equilibria in quasi-homogeneous three bod…
We introduce an algebraic method to study local stability in the Newtonian $n$-body problem when certain symmetries are present. We use representation theory of groups to simplify the calculations of certain eigenvalue problems. The method…
For many-body systems with short range interaction a series of relations were derived connecting many properties of the system to the dynamics of a closely packed few-body subsystems. Some of these relations were experimentally verified in…
We study the stationary points of the hierarchical three body problem in the planetary limit (m_2, m_3 << m_1) at both the quadrupole and octupole orders. We demonstrate that the extension to octupole order preserves the principal…
Solving the homogeneous Bethe-Salpeter equation directly in Minkowski space is becoming a very alive field, since, in recent years, a new approach has been introduced, and the reachable results can be potentially useful in various areas of…
Continuing work initiated in an earlier publication [Yamada, Asada, Phys. Rev. D 82, 104019 (2010)], we investigate collinear solutions to the general relativistic three-body problem. We prove the uniqueness of the configuration for given…
An interesting situation occurs when the linearized dynamics of the shape of a formally stable Hamiltonian relative equilibrium at nongeneric momentum 1:1 resonates with a frequency of the relative equilibrium's generator. In this case some…
We carry out a sequence of coordinate changes for the planar three-body problem which successively eliminate the translation and rotation symmetries, regularize all three double collision singularities and blow-up the triple collision.…
Some advantages of the algebraic approach to many body physics, based on resolvent algebras, are illustrated by the simple example of non-interacting bosons which are confined in compact regions with soft boundaries. It is shown that the…
We present a general framework for the approximation of systems of hyperbolic balance laws. The novelty of the analysis lies in the construction of suitable relaxation systems and the derivation of a delicate estimate on the relative…
A stationary stable solution of the Stokes equations for three identical heavy solid spheres falling in a vertical plane is found. It has no analog in the point-particle approximation. Three spheres aligned horizontally at equal distances…
For a system of $N$ bosons in one space dimension with two-body $\delta$-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by…
The simplest solutions of the N-body problem --symmetric relative equilibria-- are shown to be organizing centers from which stem some recently studied classes of periodic solutions. We focus on the relative equilibrium of the equal-mass…
The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…
We employ a port-Hamiltonian approach to model nonlinear rigid multibody systems subject to both position and velocity constraints. Our formulation accommodates Cartesian and redundant coordinates, respectively, and captures kinematic as…
We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…
In this work, we propose a new existence result for quasi-equilibrium problems using generalized monotonicity in an infinite dimensional space. Also, we show that the notions of generalized monotonicity can be characterized in terms of…
We give elementary applications of quasi-homomorphisms to growth problems in groups. A particular case concerns the number of torsion elements required to factorise a given element in the mapping class group of a surface.
This paper proposes a new equilibrium concept "robust perfect equilibrium" for non-cooperative games with a continuum of players, incorporating three types of perturbations. Such an equilibrium is shown to exist (in symmetric mixed…
We introduce and study the notion of relative rigidity for pairs $(X,\JJ)$ where 1) $X$ is a hyperbolic metric space and $\JJ$ a collection of quasiconvex sets 2) $X$ is a relatively hyperbolic group and $\JJ$ the collection of parabolics…
This paper concerns the investigation of the stability properties of relative equilibria which are rigidly rotating vortex configurations sometimes called vortex crystals, in the N-vortex problem. Such a configurations can be characterized…