Related papers: Closed Form Expressions for the Potentials and Acc…
I derive the statistical relationship between a radial velocity or astrometric acceleration (a trend), a companion's mass, and the projected separation of the companion. These relationships, expressed as probability density functions, are…
A closed-form expression is obtained for the density of a simple layer, equipotential to an oblate level ellipsoid of revolution in an outer space. The potential of any level spheroid of positive mass with the inward direction of attracting…
Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We…
Expressions for intermolecular forces and torques, derived from pair potentials between rigid non-spherical units, are presented. The aim is to give compact and clear expressions, which are easily generalised, and which minimise the risk of…
In this letter, we propose a general real-space method for the generation of nonparaxial accelerating beams with arbitrary predefined convex trajectories. Our results lead to closed-form expressions for the required phase at the input…
This paper explores orbits in extended mass distributions and develops an analytic approximation scheme based on epicycloids (spirograph patterns). We focus on the Hernquist potential which provides a good model for many astrophysical…
Pairs potential-density in terms of elementary functions that represents flat rings structures are presented. We study structures representing one or several concentric flat rings. Also disks surrounded by concentric flat rings are…
The phase--space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps…
A formalism is presented to obtain closed evolution equations for asymptotic probability distribution functions of turbulence magnitudes. The formalism is derived for a generic evolution equation, so that the final result can be easily…
This paper deals with the gravitational potential of a homogeneous torus with elliptical cross-section. We present a new expression for its gravitational potential which is valid in any point of the space, obtained by modeling the torus…
In this note we present complete, closed-form expressions for random relative velocities between colliding particles of arbitrary size in nebula turbulence. These results are exact for very small particles (those with stopping times much…
A useful crude approximation for Abelian functions is developed and applied to orbits. The bound orbits in the power-law potentials A*r^{-alpha} take the simple form (l/r)^k = 1 + e cos(m*phi), where k = 2 - alpha > 0 and 'l' and 'e' are…
This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.
The study of self-gravitating stellar systems has provided important hints to develop tools of analytical mechanics. In the present contribution we review how to exploit detuned resonant normal forms to extract information on several…
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…
The scalar and vector potentials of the acceleration field and the pressure field are calculated for the first time for a rotating relativistic uniform system, and the dependence of the potentials on the angular velocity is found. These…
We develop an effective model to describe the dynamics of a system of particle moving in circular configurations around a central mass, by considering the continuum limit of the angular distribution, to obtain the stable configurations for…
When modeling the three-dimensional hydrodynamics of interstellar material rotating in a galactic gravitational potential, it is useful to have an analytic expression for gravitational perturbations due to stellar spiral arms. We present…
The envelope of an elliptical Gaussian complex vector, or equivalently, the amplitude or norm of a bivariate normal random vector has application in many weather and signal processing contexts. We explicitly characterize its distribution in…
A unified parametrization of the circular velocity, which accurately fits 850 galaxy rotation curves without needing in advance the knowledge of the luminous matter components, nor a fixed dark matter halo model, is proposed. A notable…