Modifying the atlas of low lunar orbits using inert tethers

For long enough tethers, the coupling of the attitude and orbital dynamics may show non-negligible effects in the orbital motion of a tethered satellite about a central body. In the case of fast rotating tethers the attitude remains constant, on average, up to second order effects. Besides, for a tether rotating in a plane parallel to the equatorial plane of the central body, the attitude?orbit coupling effect is formally equal to the perturbation of the Keplerian motion produced by the oblateness of the central body and, therefore, may have a stabilizing effect in the orbital dynamics. In the case of a tethered satellite in a low lunar orbit, it is demonstrated that feasible tether lengths can help in modifying the actual map of lunar frozen orbits

Gromov hyperbolicity of periodic planar graphs

The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it. The main result in this paper is a very simple characterization of the hyperbolicity of a large class of periodic planar graphs.

Analysis of the railway track as a spatially periodic structure

This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartín [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de Nó and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given

Vortex pinning vs superconducting wire network: origin of periodic oscillations induced by applied magnetic fields in superconducting films with arrays of nanomagnets

Hybrid magnetic arrays embedded in superconducting films are ideal systems to study the competition between different physical (such as the coherence length) and structural length scales such as are available in artificially produced structures. This interplay leads to oscillation in many magnetically dependent superconducting properties such as the critical currents, resistivity and magnetization. These effects are generally analyzed using two distinct models based on vortex pinning or wire network. In this work, we show that for magnetic dot arrays, as opposed to antidot (i.e. holes) arrays, vortex pinning is the main mechanism for field induced oscillations in resistance R(H), critical current Ic(H), magnetization M(H) and ac-susceptibility χ ac(H) in a broad temperature range. Due to the coherence length divergence at Tc, a crossover to wire network behaviour is experimentally found. While pinning occurs in a wide temperature range up to Tc, wire network behaviour is only present in a very narrow temperature window close to Tc. In this temperature interval, contributions from both mechanisms are operational but can be experimentally distinguished.

EDROMO: An accurate propagator for elliptical orbits in the perturbed two-body problem

EDROMO is a special perturbation method for the propagation of elliptical orbits in the perturbed two-body problem. The state vector consists of a time-element and seven spatial elements, and the independent variable is a generalized eccentric anomaly introduced through a Sundman time transformation. The key role in the derivation of the method is played by an intermediate reference frame which enjoys the property of remaining fixed in space as long as perturbations are absent. Three elements of EDROMO characterize the dynamics in the orbital frame and its orientation with respect to the intermediate frame, and the Euler parameters associated to the intermediate frame represent the other four spatial elements. The performance of EDromo has been analyzed by considering some typical problems in astrodynamics. In almost all our tests the method is the best among other popular formulations based on elements.

Magnetic Attitude Control for Satellites in Polar or Sun-Synchronous Orbits

In this work, a new law for magnetic control of satellites in near-polar orbits is presented. This law has been developed for the UMPSat-2 microsatellite, which has been designed and manufactured by Universidad Politécnica de Madrid, Madrid. The control law is a modification of the B-dot strategy that enables the satellite to control the rotation rate. Besides, the satellite?s equilibrium state is characterized by having the rotation axis perpendicular to the orbit?s plane. The control law described in the present work only needs magnetometers and magnetorquers, as sensors and actuators, respectively, to carry out a successful attitude control on the spacecraft. A description of the analysis is included. Performance and applicability of the proposed method have been demonstrated by control dynamics together with Monte Carlo techniques and by implementing the control law in the UPMSat-2 mission simulator. Results show good performance in terms of acquisition and stability of the satellite rotation rate and orientation with respect to its orbit?s plane.

Periodic emission of droplets from an oscillating electrified meniscus of a low-viscosity, highly conductive liquid

The generation of identical droplets of controllable size in the micrometer range is a problem of much interest owing to the numerous technological applications of such droplets. This work reports an investigation of the regime of periodic emission of droplets from an electrified oscillating meniscus of a liquid of low viscosity and high electrical conductivity attached to the end of a capillary tube, which may be used to produce droplets more than ten times smaller than the diameter of the tube. To attain this periodic microdripping regime, termed axial spray mode II by Juraschek and Röllgen [R. Juraschek and F. W. Röllgen, Int. J. Mass Spectrom. 177, 1 (1998)], liquid is continuously supplied through the tube at a given constant flow rate, while a dc voltage is applied between the tube and a nearby counter electrode. The resulting electric field induces a stress at the surface of the liquid that stretches the meniscus until, in certain ranges of voltage and flow rate, it develops a ligament that eventually detaches, forming a single droplet, in a process that repeats itself periodically. While it is being stretched, the ligament develops a conical tip that emits ultrafine droplets, but the total mass emitted is practically contained in the main droplet. In the parametrical domain studied, we find that the process depends on two main dimensionless parameters, the flow rate nondimensionalized with the diameter of the tube and the capillary time, q, and the electric Bond number BE, which is a nondimensional measure of the square of the applied voltage. The meniscus oscillation frequency made nondimensional with the capillary time, f, is of order unity for very small flow rates and tends to decrease as the inverse of the square root of q for larger values of this parameter. The product of the meniscus mean volume times the oscillation frequency is nearly constant. The characteristic length and width of the liquid ligament immediately before its detachment approximately scale as powers of the flow rate and depend only weakly on the applied voltage. The diameter of the main droplets nondimensionalized with the diameter of the tube satisfies dd≈(6/π)1/3(q/f)1/3, from mass conservation, while the electric charge of these droplets is about 1/4 of the Rayleigh charge. At the minimum flow rate compatible with the periodic regimen, the dimensionless diameter of the droplets is smaller than one-tenth, which presents a way to use electrohydrodynamic atomization to generate droplets of highly conducting liquids in the micron-size range, in marked contrast with the cone-jet electrospray whose typical droplet size is in the nanometric regime for these liquids. In contrast with other microdripping regimes where the mass is emitted upon the periodic formation of a narrow capillary jet, the present regime gives one single droplet per oscillation, except for the almost massless fine aerosol emitted in the form of an electrospray.