Related papers: On generalized median triangles and tracing orbits
We treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this setting the main result of [4] is applicable. This guarantees…
Generalized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in the study of spectral curves and…
The traditional approach to analyzing mean motion resonances is through canonical perturbation theory. While this is a powerful method, its generality leads to complicated combinations of variables that are challenging to interpret and…
The correspondence between 2-parameter families of oriented lines in ${\Bbb{R}}^3$ and surfaces in $T{\Bbb{P}}^1$ is studied, and the geometric properties of the lines are related to the complex geometry of the surface. Congruences…
Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning radius of convergence…
We study the general rational trigonometry of a tetrahedron, based on quadrances, spreads and solid spreads, using vector products associated to an arbitrary symmetric bilinear form over a general field, not of characteristic two. This…
Most genuine multi-sided surface representations depend on a 2D domain that enables a mapping between local parameters and global coordinates. The shape of this domain ranges from regular polygons to curved configurations, but the simple…
In this document, we study the interaction between different geometric structures that can be defined as morphisms of sections of the generalized tangent bundle $\mathbb TM:= TM\oplus T^*M\to M$. In particular, we show the behaviour of…
A family of periodic orbits is proven to exist in the spatial lunar problem that are continuations of a family of consecutive collision orbits, perpendicular to the primary orbit plane. This family emanates from all but two energy values.…
We study groups generated by three half-turns in the Lobachevsky $3$-space and their quotient orbifolds. These generalized triangle groups are closely related to the arbitrary 2-generator Kleinian groups. Our main result is a classification…
We compute the equivariant fundamental class of the orbit closure of a linear series on the projective line. We also describe the boundary of the orbit closure and how the orbits specialise in one parameter families.
Multiplicities of periodic orbit lengths for non-arithmetic Hecke triangle groups are discussed. It is demonstrated both numerically and analytically that at least for certain groups the mean multiplicity of periodic orbits with exactly the…
A systematic study of closed classical orbits of the hydrogen atom in crossed electric and magnetic fields is presented. We develop a local bifurcation theory for closed orbits which is analogous to the well-known bifurcation theory for…
The angular and the radial parts of the dynamics of the perturbed Kepler motion are separable in many important cases. In this paper we study the radial motion and its parametrizations. We develop in detail a generalized eccentric anomaly…
Given a regular $n$-gon on the plane, it is evident that from any point on the plane, taken as a center, one can draw $n$ concentric circles such that each circle passes through one of the vertices of the polygon. Naturally, this raises the…
We investigate the motions of a bar structure consisting of two congruent tetrahedra, whose edges in their basic position form the face diagonals of a rectangular parallelepiped. The constraint of the motion is that the originally…
We obtain universal affine type estimates for the location of the geometric medians of triangle perimeters and for the location of the geometric medians of triangular domains. At the end, some alternative implementations of the triangle…
Percolation on a plane is usually associated with clusters spanning two opposite sides of a rectangular system. Here we investigate three-leg clusters generated on a square lattice and spanning the three sides of equilateral triangles. If…
In this paper the problem of finding a normal form of triangles and plane quadrilaterals up to similarity is considered. Several normal forms for triangles and a normal form for quadrilaterals of special case are described. Normal forms of…
Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…