Analytical investigation of the dynamics of tethered constellations in Earth orbit, phase 2

This Quarterly Report deals with the deployment maneuver of a single-axis, vertical constellation with three masses. A new, easy to handle, computer code that simulates the two-dimensional dynamics of the constellation has been implemented. This computer code is used for designing control laws for the deployment maneuver that minimizes the acceleration level of the low-g platform during the maneuver

Sensitivity Analysis of an Automated Calibration Routine for Airborne Cameras

Given a known aircraft location, a set of camera calibration parameters can be used to correlate features in an image with ground locations. Previously, these calibration parameters were obtained during preflight with a lengthy calibration process. A method to automate this calibration using images taken with an aircraft mounted camera and position and attitude data is developed. This thesis seeks to determine a partial set of circumstances that affect the accuracy of the calibration results through simulation and experimental flight test. A software simulator is developed in which to test an array of aircraft maneuvers, camera orientations, and noise injection. Results from the simulation are used to prepare test points for an experiment flight test conducted to validate the calibration algorithm and the simulator. Real world flight test methodology and results are discussed. Images of the ground along with precise aircraft navigation and time data were gathered and processed for several representative aircraft maneuvers using two camera orientations

The investigation of tethered satellite system dynamics

A progress report is presented that deals with three major topics related to Tethered Satellite System Dynamics. The SAO rotational dynamics computer code was updated. The program is now suitable to deal with inclined orbits. The output has been also modified in order to show the satellite Euler angles referred to the rotating orbital frame. The three-dimensional high resolution computer program SLACK3 was developed. The code simulates the three-dimensional dynamics of a tether going slack taking into account the effect produced by boom rotations. Preliminary simulations on the three-dimensional dynamics of a recoiling slack tether are shown in this report. A program to evaluate the electric potential around a severed tether is immersed in a plasma. The potential is computed on a three-dimensional grid axially symmetric with respect to the tether longitudinal axis. The electric potential variations due to the plasma are presently under investigation

Analytical investigation of the dynamics of tethered constellations in earth orbit

This Quarterly Report on Tethering in Earth Orbit deals with three topics: (1) Investigation of the propagation of longitudinal and transverse waves along the upper tether. Specifically, the upper tether is modeled as three massive platforms connected by two perfectly elastic continua (tether segments). The tether attachment point to the station is assumed to vibrate both longitudinally and transversely at a given frequency. Longitudinal and transverse waves propagate along the tethers affecting the acceleration levels at the elevator and at the upper platform. The displacement and acceleration frequency-response functions at the elevator and at the upper platform are computed for both longitudinal and transverse waves. An analysis to optimize the damping time of the longitudinal dampers is also carried out in order to select optimal parameters. The analytical evaluation of the performance of tuned vs. detuned longitudinal dampers is also part of this analysis. (2) The use of the Shuttle primary Reaction Control System (RCS) thrusters for blowing away a recoiling broken tether is discussed. A microcomputer system was set up to support this operation. (3) Most of the effort in the tether plasma physics study was devoted to software development. A particle simulation code has been integrated into the Macintosh II computer system and will be utilized for studying the physics of hollow cathodes

System engineering study of electrodynamic tether as a spaceborne generator and radiator of electromagnetic waves in the ULF/ELF frequency band

The transmission and generation by orbiting tethered satellite systems of information carrying electromagnetic waves in the ULF/ELF frequency band to the Earth at suitably high signal intensities was examined and the system maintaining these intensities in their orbits for long periods of time without excessive onboard power requirements was investigated. The injection quantity power into electromagnetic waves as a function of system parameters such as tether length and orbital height was estimated. The basic equations needed to evaluate alternataing current tethered systems for external energy requirements are presented. The energy equations to tethered systems with various lengths, tether resistances, and radiation resistances, operating at different current values are applied. Radiation resistance as a function of tether length and orbital height is discussed. It is found that ULF/ELF continuously radiating systems could be maintained in orbit with moderate power requirements. The effect of tether length on the power going into electromagnetic waves and whether a single or dual tether system is preferable for the self-driven mode is discussed. It is concluded that the single tether system is preferable over the dual system

Ab initio determination of an extended Heisenberg Hamiltonian in CuO2 layers

Accurate ab initio calculations on embedded Cu_4O_{12} square clusters, fragments of the La_2CuO_4 lattice, confirm a value of the nearest neighbor antiferromagnetic coupling (J=124 meV) previously obtained from ab initio calculations on bicentric clusters and in good agreement with experiment. These calculations predict non negligible antiferromagnetic second-neighbor interaction (J'=6.5 meV) and four-spin cyclic exchange (K=14 meV), which may affect the thermodynamic and spectroscopic properties of these materials. The dependence of the magnetic coupling on local lattice distortions has also been investigated. Among them the best candidate to induce a spin-phonon effect seems to be the movement of the Cu atoms, changing the Cu-Cu distance, for which the variation of the nearest neighbor magnetic coupling with the Cu-O distance is {\Delta J}/{\Delta d_{Cu-O}}\sim 1700 cm^{-1} A^{-1}.Comment: 11 pages, 5 figures, submitted to Phys. Rev.

The investigation of tethered satellite system dynamics

The analysis of the rotational dynamics of the satellite was focused on the rotational amplitude increase of the satellite, with respect to the tether, during retrieval. The dependence of the rotational amplitude upon the tether tension variation to the power 1/4 was thoroughly investigated. The damping of rotational oscillations achievable by reel control was also quantified while an alternative solution that makes use of a lever arm attached with a universal joint to the satellite was proposed. Comparison simulations between the Smithsonian Astrophysical Observatory and the Martin Marietta (MMA) computer code of reteival maneuvers were also carried out. The agreement between the two, completely independent, codes was extremely close, demonstrating the reliability of the models. The slack tether dynamics during reel jams was analytically investigated in order to identify the limits of applicability of the SLACK3 computer code to this particular case. Test runs with SLACK3 were also carried out

On the Sandpile group of the cone of a graph

In this article, we give a partial description of the sandpile group of the cone of the cartesian product of graphs in function of the sandpile group of the cone of their factors. Also, we introduce the concept of uniform homomorphism of graphs and prove that every surjective uniform homomorphism of graphs induces an injective homomorphism between their sandpile groups. As an application of these result we obtain an explicit description of a set of generators of the sandpile group of the cone of the hypercube of dimension d.Comment: 20 pages, 11 figures. The title was changed, other impruvements were made throughout the article. To appear in Linear Algebra and Its Application

Tether Transportation System Study

The projected traffic to geostationary earth orbit (GEO) is expected to increase over the next few decades. At the same time, the cost of delivering payloads from the Earth's surface to low earth orbit (LEO) is projected to decrease, thanks in part to the Reusable Launch Vehicle (RLV). A comparable reduction in the cost of delivering payloads from LEO to GEO is sought. The use of in-space tethers, eliminating the requirement for traditional chemical upper stages and thereby reducing the launch mass, has been identified as such an alternative. Spinning tethers are excellent kinetic energy storage devices for providing the large delta vee's required for LEO to GEO transfer. A single-stage system for transferring payloads from LEO to GEO was proposed some years ago. The study results presented here contain the first detailed analyses of this proposal, its extension to a two-stage system, and the likely implementation of the operational system