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Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…
The hierarchical triple body approximation has useful applications to a variety of systems from planetary and stellar scales to supermassive black holes. In this approximation, the energy of each orbit is separately conserved and therefore…
Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite…
The hierarchical three-body problem has many applications in relativistic astrophysics, and can play an important role in the formation of the binary black hole mergers detected by LIGO/Virgo. However, many studies have only included…
An analytical solution to the the three-dimensional telegraph equation is presented. This equation has recently received some attention but so far the treatment has been one-dimensional. By using the structural similarity to the…
For Reeb vector fields on closed 3-manifolds, cylindrical contact homology is used to show that the existence of a set of closed Reeb orbit with certain knotting/linking properties implies the existence of other Reeb orbits with other…
We introduce and study a new 3d Topological Field Theory which can be associated to any compact real manifold X. This TFT is analogous to the 2d A-model and reduces to it upon compactification on an interval with suitable boundary…
In this paper, we prove that the linearized system of elliptic triangle homographic solution of planar charged three-body problem can be transformed to that of the elliptic equilateral triangle solution of the planar classical three-body…
The coordinate conditions for three exact solutions for the metric components of a coordinate system with constant acceleration or of a static plane symmetric gravitational field are presented. First, the coordinate condition that the…
GYOTO, a general relativistic ray-tracing code, is presented. It aims at computing images of astronomical bodies in the vicinity of compact objects, as well as trajectories of massive bodies in relativistic environments. This code is…
Modern applications of celestial mechanics include the study of closely packed systems of exoplanets, circumbinary planetary systems, binary-binary interactions in star clusters, and the dynamics of stars near the galactic centre. While…
A new approach to special relativity is presented which introduces coordinate systems with imaginary time axes, observation systems, and coordinate bases.
Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories…
In a previous paper (Gayon & Bois 2008a), we have shown the general efficiency of retrograde resonances for stabilizing compact planetary systems. Such retrograde resonances can be found when two-planets of a three-body planetary system are…
We present a geometric approach to the three-body problem in the non-relativistic context of the Barbour-Bertotti theories. The Riemannian metric characterizing the dynamics is analyzed in detail in terms of the relative separations.…
This paper proposes the geometric relationship of epipolar geometry and orientation- and scale-covariant, e.g., SIFT, features. We derive a new linear constraint relating the unknown elements of the fundamental matrix and the orientation…
We establish the hierarchy among twelve equivalence relations (similarities) on the class of relational structures: the equality, the isomorphism, the equimorphism, the full relation, four similarities of structures induced by similarities…
We introduce some analytic relations on the set of partial differential equations of two variables. It relies on a new comparison method to give rough asymptotic estimates for solutions which obey different partial differential equations.…
In this paper, a function on any pair of graphs is defined whose properties are similar to the properties of dot product in vector space. This function enables us to define graph orthogonality and, also, a new metric on isomorphism classes…
We study equivalence relation of the set of triangles generated by similarity and operation on a triangle to get a new one by joining division points of three edges with the same ratio. Using the moduli space of similarity classes of…