Related papers: A Novel Orbit Parameterization in Spherical Coordi…
A novel spherical convolution is defined through the sifting property of the Dirac delta on the sphere. The so-called sifting convolution is defined by the inner product of one function with a translated version of another, but with the…
Three parameterizations are developed for modeling translational motion of a point mass in atmosphere flight over a central rotating body. Unlike well-known parameterizations such as spherical coordinate parameterizations, where position…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…
A Dyson ring is a hypothetical megastructure, that a very advanced civilization would build around a star to harness more of its energy. Satellite propagation is of high priority in such a vast world where distances could very well be…
We study generalization of median triangles on the plane with two complex parameters. By specialization of the parameters, we produce periodical motion of a triangle whose vertices trace each other on a common closed orbit.
This paper examines options for orbit configurations for a space interferometer. In contrast to previously presented concepts for space very long baseline interferometry, we propose a combination of regular and retrograde near-Earth…
A new approach to special relativity is presented which introduces coordinate systems with imaginary time axes, observation systems, and coordinate bases.
We describe a method to obtain spherical parameterizations of arbitrary data through the use of persistent cohomology and variational optimization. We begin by computing the second-degree persistent cohomology of the filtered Vietoris-Rips…
This paper presents a novel algorithm to incorporate orbital parameters into radar ambiguity function expressions by extending the standard ambiguity function to match Keplerian two-body orbits. A coherent orbital matched-filter will…
The space of phase-parameters (sky-position, frequency, spindowns) of a coherent matched-filtering search for continuous gravitational waves from isolated neutron stars shows strong global correlations (``circles in the sky''). In the local…
In this paper, we study the configuration space of orbits, a generalization of the configuration space of points but for algebraic varieties that are acted by an algebraic reductive group. The main objective of this work is to study the…
Recent microscopy imaging techniques allow to precisely analyze cell morphology in 3D image data. To process the vast amount of image data generated by current digitized imaging techniques, automated approaches are demanded more than ever.…
If an orbit is fitted from combined RV and astrometric data, the orbit should be physically consistent with both data sets. The Keplerian orbit of a planet is a highly nonlinear function of seven parameters. The astrometric orbit problem…
The main problem is to understand and to find periodic symmetric orbits in the $n$-body problem, in the sense of finding methods to prove or compute their existence, and more importantly to describe their qualitative and quantitative…
Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is…
We present a procedure for determination of positions and orbital elements, and associated uncertainties, of outer Solar System planets. The orbit-fitting procedure is greatly streamlined compared to traditional methods because acceleration…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
The new approach of the regular spacing of planetary orbits and planet mass distribution in the Solar system is considered. The relative planetary distances will be represented as the inverse composite probabilities of two discrete…
The parameterization of open and closed anatomical surfaces is of fundamental importance in many biomedical applications. Spherical harmonics, a set of basis functions defined on the unit sphere, are widely used for anatomical shape…