Analytical attitude propagation with non-singular variables and gravity gradient torque for spin stabilized satellite

An analytical approach for the spin stabilized satellite attitude propagation is presented using the non-singular canonical variables to describe the rotational motion. Two sets of variables were introduced for Fukushima in 1994 by a canonical transformation and they are useful when the angle between z-satellite axis of a coordinate system fixed in artificial satellite and the rotational angular momentum vector is zero or when the angle between Z-equatorial axis and rotation angular momentum vector is zero. Analytical solutions for rotational motion equations and torque-free motion are discussed in terms of the elliptic functions and by the application of some simplification to get an approximated solution. These solutions are compared with a numerical solution and the results show a good agreement for many rotation periods. When the mean Hamiltonian associated with the gravity gradient torque is included, an analytical solution is obtained by the application of the successive approximations' method for the satellite in an elliptical orbit. These solutions show that the magnitude of the rotation angular moment is not affected by the gravity gradient torque but this torque causes linear and periodic variations in the angular variables, long and short periodic variations in Z-equatorial component of the rotation angular moment and short periodic variations in x-satellite component of the rotation angular moment. The goal of this analysis is to emphasize the geometrical and physical meaning of the non-singular variables and to validate the approximated analytical solution for the rotational motion without elliptic functions for a non-symmetrical satellite. The analysis can be applied for spin stabilized satellite and in this case the general solution and the approximated solution are coincidence. Then the results can be used in analysis of the space mission of the Brazilian Satellites. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Spin stabilized satellite's attitude propagation with quaternions

This paper presents a study of a modeling scheme for the spin stabilized satellites attitude, entirely developed in terms of quaternion parametrization. The analysis includes numerical propagation of the rotational motion equation, considering the influence of the following torques: aerodynamic, gravity gradient, residual magnetic, eddy currents and the one due to the Lorentz force. Applications are developed considering the Brazilian Spin Stabilized Satellites SCD1 and SCD2, which are quite appropriated for verification and comparison of the theory with the real data generated and processed by the INPE's Satellite Control Center (SCC). The results show that for SCD1 and SCD2 the influence of the eddy current torque is bigger than the others ones, not only due to the orbit altitude, but also to other specific satellites characteristics. The influence of the torque due to Lorentz force is smaller than the others ones because of the dimension and the electrical charges of the SCD1 and SCD2. In all performed tests the errors remained within the dispersion range specified for the attitude determination system of INPE's SCC. The results show the feasibility of using the quaternion attitude parametrization for modeling the satellite dynamics of spin stabilized satellites.

Spin stabilized satellite's attitude analytical prediction

An analytical approach for spin stabilized attitude propagation is presented, considering the coupled effect of the aerodynamic torque and the gravity gradient torque. A spherical coordination system fixed in the satellite is used to locate the satellite spin axis in relation to the terrestrial equatorial system. The spin axis direction is specified by its right ascension and the declination angles and the equation of motion are described by these two angles and the magnitude of the spin velocity. An analytical averaging method is applied to obtain the mean torques over an orbital period. To compute the average components of both aerodynamic torque and the gravity gradient torque in the satellite body frame reference system, an average time in the fast varying orbit element, the mean anomaly, is utilized. Afterwards, the inclusion of such torques on the rotational motion differential equations of spin stabilized satellites yields conditions to derive an analytical solution. The pointing deviation evolution, that is, the deviation between the actual spin axis and the computed spin axis, is also availed. In order to validate the analytical approach, the theory developed has been applied for spin stabilized Brazilian satellite SCD1, which are quite appropriated for verification and comparison of the data generated and processed by the Satellite Control Center of the Brazil National Research Institute (INPE). Numerical simulations performed with data of Brazilian Satellite SCD1 show the period that the analytical solution can be used to the attitude propagation, within the dispersion range of the attitude determination system performance of Satellite Control Center of the Brazilian Research Institute.

Analytical prediction of the spin stabilized satellite's attitude using the solar radiation torque

The aim of this paper is to present an analytical solution for the spin motion equations of spin-stabilized satellite considering only the influence of solar radiation torque. The theory uses a cylindrical satellite on a circular orbit and considers that the satellite is always illuminated. The average components of this torque were determined over an orbital period. These components are substituted in the spin motion equations in order to get an analytical solution for the right ascension and declination of the satellite spin axis. The time evolution for the pointing deviation of the spin axis was also analyzed. These solutions were numerically implemented and compared with real data of the Brazilian Satellite of Data Collection - SCD1 an SCD2. The results show that the theory has consistency and can be applied to predict the spin motion of spin-stabilized artificial satellites.

Analytical attitude prediction of spin stabilized spacecrafts perturbed by magnetic residual torque

An analytical approach for spin-stabilized spacecraft attitude prediction is presented for the influence of the residual magnetic torques. Assuming an inclined dipole model for the Earth's magnetic field, an analytical averaging method is applied to obtain the mean residual torque every orbital period. The orbit mean anomaly is utilized to compute the average components of residual torque in the spacecraft body frame reference system. The theory is developed for time variations in the orbital elements, and non-circular orbits, giving rise to many curvature integrals. It is observed that the residual magnetic torque does not have component along the spin axis. The inclusion of this torque on the rotational motion differential equations of a spin stabilized spacecraft yields conditions to derive an analytical solution. The solution shows that residual torque does not affect the spin velocity magnitude, contributing only for the precession and the drift of the spin axis of the spacecraft. (c) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

Spin-Stabilized Spacecrafts: Analytical Attitude Propagation Using Magnetic Torques

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Influence of the resonance in a gravity-gradient stabilized satellite

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Propagação da atitude de satélites artificiais estabilizados por rotação: torque residual médio com o modelo de quadripolo para o campo geomagnético

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Geostationary Earth Radiation Budget Project

This paper reports on a new satellite sensor, the Geostationary Earth Radiation Budget (GERB) experiment. GERB is designed to make the first measurements of the Earth's radiation budget from geostationary orbit. Measurements at high absolute accuracy of the reflected sunlight from the Earth, and the thermal radiation emitted by the Earth are made every 15 min, with a spatial resolution at the subsatellite point of 44.6 km (north–south) by 39.3 km (east–west). With knowledge of the incoming solar constant, this gives the primary forcing and response components of the top-of-atmosphere radiation. The first GERB instrument is an instrument of opportunity on Meteosat-8, a new spin-stabilized spacecraft platform also carrying the Spinning Enhanced Visible and Infrared (SEVIRI) sensor, which is currently positioned over the equator at 3.5°W. This overview of the project includes a description of the instrument design and its preflight and in-flight calibration. An evaluation of the instrument performance after its first year in orbit, including comparisons with data from the Clouds and the Earth's Radiant Energy System (CERES) satellite sensors and with output from numerical models, are also presented. After a brief summary of the data processing system and data products, some of the scientific studies that are being undertaken using these early data are described. This marks the beginning of a decade or more of observations from GERB, as subsequent models will fly on each of the four Meteosat Second Generation satellites.

Predição analítica do movimento rotacional de satélites estabilizados por rotação

Pós-graduação em Física - FEG

Satélites estabilizados por rotação: torques externos e ângulo de aspecto solar

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Satelites estabilizados por rotação e torque magnético residual

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Satélites estabilizados por rotação e torque de radiação solar direta

The aims of this work are to analyze the direct solar radiation pressure torque (TPRS) in the rotational motion of spin-stabilized artificial satellites, to numerically implement these solutions and to compare the results with real data of the Brazilian Satellite Data Collection – SCD1 and SCD2, supplied by INPE. The mathematical model for this torque is determined for a cylindrical satellite, and the components of this torque are determined in a fixed system in the satellite. An analytical solution for the spin motion equations is proposed, in which TPRSD does not affect the spin velocity of the satellite. Two approaches are adopted in the numerical implementation of the developed theory: the first one considers the proposed theory and the second introduces a variation in the spin velocity based on its real variation. The results obtained indicate that the solar radiation pressure torque has little influence in the right ascension and declination axis of rotation due to the small dimension of the satellite and altitude in which it is found. To better validate the application of the presented theory, the angular deviation of the spin axis and solar aspect angle were also analyzed. The comparison of the results of the approaches conducted with real data show good precision in the theory, which can be applied in the prediction of the rotational motion of the spin-stabilized artificial satellites, when others external torques are considered besides the direct solar radiation pressure torque

Exotic phases induced by strong spin-orbit coupling in ordered double perovskites

We construct and analyze a microscopic model for insulating rocksalt ordered double perovskites, with the chemical formula A(2)BB'O(6), where the B' atom has a 4d(1) or 5d(1) electronic configuration and forms a face-centered-cubic lattice. The combination of the triply degenerate t(2g) orbital and strong spin-orbit coupling forms local quadruplets with an effective spin moment j=3/2. Moreover, due to strongly orbital-dependent exchange, the effective spins have substantial biquadratic and bicubic interactions (fourth and sixth order in the spins, respectively). This leads, at the mean-field level, to three main phases: an unusual antiferromagnet with dominant octupolar order, a ferromagnetic phase with magnetization along the [110] direction, and a nonmagnetic but quadrupolar ordered phase, which is stabilized by thermal fluctuations and intermediate temperatures. All these phases have a two-sublattice structure described by the ordering wave vector Q=2 pi(001). We consider quantum fluctuations and argue that in the regime of dominant antiferromagnetic exchange, a nonmagnetic valence-bond solid or quantum-spin-liquid state may be favored instead. Candidate quantum-spin-liquid states and their basic properties are described. We also address the effect of single-site anisotropy driven by lattice distortions. Existing and possible future experiments are discussed in light of these results.

Control of chaotic motion in a dual-spin spacecraft with nutational damping

Control of chaotic vibrations in a dual-spin spacecraft with an axial nutational damper is achieved using two techniques. The control methods are implemented on two realistic spacecraft parameter configurations that have been found to exhibit chaotic instability when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitudes and frequencies. Such a torque, in practice, may arise under malfunction of the control system or from an unbalanced rotor. Chaotic instabilities arising from these torques could introduce uncertainties and irregularities into a spacecraft's attitude motion and, consequently, could have disastrous effects on its operation. The two control methods, recursive proportional feedback and continuous delayed feedback, are recently developed techniques for control of chaotic motion in dynamic systems. Each technique is outlined and the effectiveness on this model compared and contrasted. Numerical simulations are performed, and the results are studied by means of time history, phase space, Poincare map, Lyapunov characteristic exponents, and bifurcation diagrams.