A Special Perturbation Method in Orbital Dynamics

Bead models are used in dynamical simulation of tethers. These models discretize a cable using beads distributed along its length. The time evolution is obtained nu- merically. Typically the number of particles ranges between 5 and 50, depending on the required accuracy. Sometimes the simulation is extended over long periods (several years). The complex interactions between the cable and its spatial environment require to optimize the propagators —both in runtime and precisión that constitute the central core of the process. The special perturbation method treated on this article conjugates simpleness of computer implementation, speediness and precision, and is capable to propagate the orbit of whichever material particle. The paper describes the evolution of some orbital elements, which are constants in a non-perturbed problem, but which evolve in the time scale imposed by the perturbation. It can be used with any kind of orbit and it is free of sin- gularities related to small inclination and/or small eccentricity. The use of Euler parameters makes it robust.

A repairability index for reinforced concrete members based on fracture mechanics

This paper proposes a repairability index for damage assessment in reinforced concrete structural members. The procedure discussed in this paper differs from the standard methods in two aspects: the structural and damage analyses are coupled and it is based on the concepts of fracture and continuum damage mechanics. The relationship between the repairability index and the well-known Park and Ang index is shown in some particular cases.

Asymptotic solution for the two-body problem with constant tangencial acceleration

An analytical solution of the two body problem perturbed by a constant tangential acceleration is derived with the aid of perturbation theory. The solution, which is valid for circular and elliptic orbits with generic eccentricity, describes the instantaneous time variation of all orbital elements. A comparison with high-accuracy numerical results shows that the analytical method can be effectively applied to multiple-revolution low-thrust orbit transfer around planets and in interplanetary space with negligible error.

Foundations and applications of non-equilibrium statistical mechanics

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Orbital debris mitigation through deorbiting with passive electrodynamic drag

The increase of orbital debris and the consequent proliferation of smaller objects through fragmentation are driving the need for mitigation strategies. The issue is how to deorbit the satellite with an efficient system that does not impair drastically the propellant budget of the satellite and, consequently, reduces its operating life. We have been investigating, in the framework of a European-Community-funded project, a passive system that makes use of an electrodynamics tether to deorbit a satellite through Lorentz forces. The deorbiting system will be carried by the satellite itself at launch and deployed from the satellite at the end of its life. From that moment onward the system operates passively without requiring any intervention from the satellite itself. The paper summarizes the results of the analysis carried out to show the deorbiting performance of the system starting from different orbital altitudes and inclinations for a reference satellite mass. Results can be easily scaled to other satellite masses. The results have been obtained by using a high-fidelity computer model that uses the latest environmental routines for magnetic field, ionospheric density, atmospheric density and a gravity field model. The tether dynamics is modelled by considering all the main aspects of a real system as the tether flexibility and its temperature-dependent electrical conductivity. Temperature variations are computed by including all the major external and internal input fluxes and the thermal flux emitted from the tether. The results shows that a relatively compact and light system can carry out the complete deorbit of a relatively large satellite in a time ranging from a month to less than a year starting from high LEO with the best performance occurring at low orbital inclinations.

Self Learning and self evaluation exercises database in basic mechanics: a theoretical-practical approach

In the School of Mines of the Technical University of Madrid (UPM) the first course of different degrees has been implemented and adapted to the European Higher Educational Area (EHEA). In all of the degrees there is a first semester course which gathers all the contents of basic mechanics: from the first kinematics concepts to the rigid solid plane motion Before the Bologna process took place, the authors had established the final assessment of the theoretical contents through open questions of theoretical-practical character In the present work, the elaboration of a wide database containing theoretical-practical questions that students can access on line is presented. The questions are divided in thirteen different questionnaires composed of a number of questions randomly chosen from a certain group in the database. Each group corresponds to a certain learning objective that the student knows. After answering the questionnaire and checking the grade assigned according to the performance of the student, the pupils can see the correct response displayed on the screen and widely explained by the professors. This represents a 10% of the final grade. As the student can access the questionnaires as many times as they want, the main goal is the self-assessment of each learning objective and therefore, getting the students involved in their own learning process so they can decide how much time they need to acquire the required level.

The orbital-motion-limited regime of cylindrical Langmuir probes

An asymptotic analysis of electron collection at high bias Fp serves to determine the domain of validity of the orbital-motion-limited regime of cylindrical Langmuir probes, which is basic for the workings of conductive bare tethers. The radius of a wire collecting OML current in an unmagnetized plasma at rest cannot exceed a value, Rmax , which is found to exhibit a minimum as a function of Fp ; atFp values of interest, Rmax is already increasing and is larger than the electron Debye length lDe . The breakdown of the regime relates to conditions far fromthe probe, at electron energies comparable to the ion thermal energy, kTi ; Rmax is found to increase with Ti . It is also found that ~1! the maximumwidth of a thin tape, if used instead of a wire, is 4Rmax ; ~2! the electron thermal gyroradius must be larger than both R and lDe for magnetic effects to be negligible; and ~3! conditions applying to the tether case are such that trapped-orbit effects are negligible.

Cylindrical Langmuir probes beyond the orbital-motion-limited regime

The current I to a cylindrical probe at rest in an unmagnetized plasma, with probe bias highly positive, is determined. The way I lags behind the orbital-motion-limited OMLcurrent, 1 OML R, as the radius R exceeds the maximum radius for the OML regime to hold, is of interest for space-tether applications. The ratio I/I OML is roughly a decreasing function of R/lD R max /lDe , which is independent of bias, with lDe the electron Debye length and Rmax /l De roughly an increasing function of the temperature ratio, Ti /Te. The dependence of current on ion energy is used to discuss the effect of probe motion through the plasma, a case applying to tethers in low orbit.

B.I.E.M. in solid mechanics

In solid mechanics the weak formulation produces an integral equation ready for a discretization and with less restrictive requiremets than the standard field equations. Fundamentally the weak formulation is a expresion of a green formula. An alternative is to choose another green formula materializing a reciprocity relationship between the basis unknowns and an auxiliary family of functions. The degree of smoothness requiered to practice the discretization is then translated to the auxiliar functions. The subsequent discretization (constant, linear etc.)produces a set of equations on the boundary of the domain. For linear 3-D problems the BIEM appears then as a powerful alternative to FEM, because of the reduction to 2-D thanks to the features previously described.

Accurate analytical approximation of asteroid deflection with constant tangential thrust

We present analytical formulas to estimate the variation of achieved deflection for an Earth-impacting asteroid following a continuous tangential low-thrust deflection strategy. Relatively simple analytical expressions are obtained with the aid of asymptotic theory and the use of Peláez orbital elements set, an approach that is particularly suitable to the asteroid deflection problem and is not limited to small eccentricities. The accuracy of the proposed formulas is evaluated numerically showing negligible error for both early and late deflection campaigns. The results will be of aid in planning future low-thrust asteroid deflection missions

Frozen orbits for scientific missions using rotating tethers

We derive a semi-analytic formulation that permits to study the long-term dynamics of fast-rotating inert tethers around planetary satellites. Since space tethers are extensive bodies they generate non-keplerian gravitational forces which depend solely on their mass geometry and attitude, that can be exploited for controlling science orbits. We conclude that rotating tethers modify the geometry of frozen orbits, allowing for lower eccentricity frozen orbits for a wide range of orbital inclination, where the length of the tether becomes a new parameter that the mission analyst may use to shape frozen orbits to tighter operational constraints.

A computational model coupling mechanics and electrophysiology in spinal cord injury

Traumatic brain injury and spinal cord injury have recently been put under the spotlight as major causes of death and disability in the developed world. Despite the important ongoing experimental and modeling campaigns aimed at understanding the mechanics of tissue and cell damage typically observed in such events, the differenti- ated roles of strain, stress and their corresponding loading rates on the damage level itself remain unclear. More specif- ically, the direct relations between brain and spinal cord tis- sue or cell damage, and electrophysiological functions are still to be unraveled. Whereas mechanical modeling efforts are focusing mainly on stress distribution and mechanistic- based damage criteria, simulated function-based damage cri- teria are still missing. Here, we propose a new multiscale model of myelinated axon associating electrophysiological impairment to structural damage as a function of strain and strain rate. This multiscale approach provides a new framework for damage evaluation directly relating neuron mechanics and electrophysiological properties, thus provid- ing a link between mechanical trauma and subsequent func- tional deficits.

Development and implementation of a virtual laboratory for training process improvement in the mechanics of continuous media

The project arises from the need to develop improved teaching methodologies in field of the mechanics of continuous media. The objective is to offer the student a learning process to acquire the necessary theoretical knowledge, cognitive skills and the responsibility and autonomy to professional development in this area. Traditionally the teaching of the concepts of these subjects was performed through lectures and laboratory practice. During these lessons the students attitude was usually passive, and therefore their effectiveness was poor. The proposed methodology has already been successfully employed in universities like University Bochum, Germany, University the South Australia and aims to improve the effectiveness of knowledge acquisition through use by the student of a virtual laboratory. This laboratory allows to adapt the curricula and learning techniques to the European Higher Education and improve current learning processes in the University School of Public Works Engineers -EUITOP- of the Technical University of Madrid -UPM-, due there are not laboratories in this specialization. The virtual space is created using a software platform built on OpenSim, manages 3D virtual worlds, and, language LSL -Linden Scripting Language-, which imprints specific powers to objects. The student or user can access this virtual world through their avatar -your character in the virtual world- and can perform practices within the space created for the purpose, at any time, just with computer with internet access and viewfinder. The virtual laboratory has three partitions. The virtual meeting rooms, where the avatar can interact with peers, solve problems and exchange existing documentation in the virtual library. The interactive game room, where the avatar is has to resolve a number of issues in time. And the video room where students can watch instructional videos and receive group lessons. Each audiovisual interactive element is accompanied by explanations framing it within the area of knowledge and enables students to begin to acquire a vocabulary and practice of the profession for which they are being formed. Plane elasticity concepts are introduced from the tension and compression testing of test pieces of steel and concrete. The behavior of reticulated and articulated structures is reinforced by some interactive games and concepts of tension, compression, local and global buckling will by tests to break articulated structures. Pure bending concepts, simple and composite torsion will be studied by observing a flexible specimen. Earthquake resistant design of buildings will be checked by a laboratory test video.

Jupiter power generation with electrodynamic tethers at constant orbital energy

An electrodynamic tether system for power generation at Jupiter is presented that allows extracting energy from Jupiter's corotating plasmasphere while leaving the system orbital energy unaltered to first order. The spacecraft is placed in a polar orbit with the tether spinning in the orbital plane so that the resulting Lorentz force, neglecting Jupiter's magnetic dipole tilt, is orthogonal to the instantaneous velocity vector and orbital radius, hence affecting orbital inclination rather than orbital energy. In addition, the electrodynamic tether subsystem, which consists of two radial tether arms deployed from the main central spacecraft, is designed in such a way as to extract maximum power while keeping the resulting Lorentz torque constantly null. The power-generation performance of the system and the effect on the orbit inclination is evaluated analytically for different orbital conditions and verified numerically. Finally, a thruster-based inclination-compensation maneuver at apoapsis is added, resulting in an efficient scheme to extract energy from the plasmasphere of the planet with minimum propellant consumption and no inclination change. A tradeoff analysis is conducted showing that, depending on tether size and orbit characteristics, the system performance can be considerably higher than conventional power-generation methods.