Spacecraft's attitude prediction: solar radiation torque and the Earth's shadow

A semi-analytical approach is proposed to study the rotational motion of an artificial satellite, under the influence of torque due to the solar radiation pressure, and taking into account the influence of Earth's shadow. Using Andoyer variables the equations for the rotational motion are presented in extended Hamiltonian form. In order to get a solution for the state variables close to an actual motion, the considered model for the shadow function takes into account physical and geometric factors and three specific regions: shadow, penumbra and full light. A mapping for the shadow function is proposed and a semi-analytical process is applied. When the satellite is totally illuminated or it is inside the penumbra, a known analytical solution is used to compute the satellite's attitude. A numerical simulation shows, when the penumbra region is included, the attenuation of the rotational motion during the transition from the shadow to the illuminate region and vice versa. (c) 2005 Published by Elsevier Ltd on behalf of COSPAR.

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.

Optimal attitude corrections for cylindrical spacecraft

A first order analytical model for optimal small amplitude attitude maneuvers of spacecraft with cylindrical symmetry in an elliptical orbits is presented. The optimization problem is formulated as a Mayer problem with the control torques provided by a power limited propulsion system. The state is defined by Seffet-Andoyer's variables and the control by the components of the propulsive torques. The Pontryagin Maximum Principle is applied to the problem and the optimal torques are given explicitly in Serret-Andoyer's variables and their adjoints. For small amplitude attitude maneuvers, the optimal Hamiltonian function is linearized around a reference attitude. A complete first order analytical solution is obtained by simple quadrature and is expressed through a linear algebraic system involving the initial values of the adjoint variables. A numerical solution is obtained by taking the Euler angles formulation of the problem, solving the two-point boundary problem through the shooting method, and, then, determining the Serret-Andoyer variables through Serret-Andoyer transformation. Numerical results show that the first order solution provides a good approximation to the optimal control law and also that is possible to establish an optimal control law for the artificial satellite's attitude. (C) 2003 COSPAR. Published by Elsevier B.V. Ltd. All rights reserved.

Attitude propagation using non-singular canonical variables

Three sets of non-singular canonical variables for the rotational motion are analyzed. These sets are useful when the angle between z-axis of a coordinate system fixed in artificial satellite ( here defined by the directions of principal moments of inertia of the satellite) and the rotational angular momentum vector is zero or when the angle between Z-inertial axis and rotational angular momentum vector is zero. The goal of this paper is to compare all these sets and to determine the benefits of their uses. With this objective, the dynamical equations of each set were derived, when mean hamiltonian associate with the gravity gradient torque is included. For the torque-free rotational motion, analytical solutions are computed for symmetrical satellite for each set of variables. When the gravity gradient torque is included, an analytical solution is shown for one of the sets and a numerical solution is obtained for one of the other sets. By this analysis we can conclude that: the dynamical equation for the first set is simple but it has neither clear geometrical nor physical meaning; the other sets have geometrical and physical meaning but their dynamical equations are more complex.

Attitude stability of artificial satellites subject to gravity gradient torque

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Spin-Stabilized Spacecrafts: Analytical Attitude Propagation Using Magnetic Torques

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Unscented Kalman Filter Applied to the Spacecraft Attitude Estimation with Euler Angles

The aim of this work is to test an algorithm to estimate, in real time, the attitude of an artificial satellite using real data supplied by attitude sensors that are on board of the CBERS-2 satellite (China Brazil Earth Resources Satellite). The real-time estimator used in this work for attitude determination is the Unscented Kalman Filter. This filter is a new alternative to the extended Kalman filter usually applied to the estimation and control problems of attitude and orbit. This algorithm is capable of carrying out estimation of the states of nonlinear systems, without the necessity of linearization of the nonlinear functions present in the model. This estimation is possible due to a transformation that generates a set of vectors that, suffering a nonlinear transformation, preserves the same mean and covariance of the random variables before the transformation. The performance will be evaluated and analyzed through the comparison between the Unscented Kalman filter and the extended Kalman filter results, by using real onboard data.

Knowledge and attitudes of health care workers from intensive care units regarding nosocomial transmission of influenza: a study on the immediate pre-pandemic period

The transmission of influenza in health care settings is a major threat to patients, especially those with severe diseases. The attitude of health care workers (HCWs) may influence the transmission of countless infections. The current study aimed to quantify knowledge and identify attitudes of HCWs involved in intensive care units (ICUs) regarding the risk of nosocomial influenza transmission. A questionnaire was applied through interviews to HCWs who worked in one of the five ICUs from a teaching hospital. Questions about influenza were deliberately dispersed among others that assessed several infectious agents. Forty-two HCWs were interviewed: nine physicians, ten nurses and 23 nursing technicians or auxiliaries. Among the 42 HCWs, 98% were aware of the potential transmission of influenza virus in the ICUs, but only 31% would indicate droplet precautions for patients with suspected infection. Moreover, only 31% of them had been vaccinated against influenza in the last campaign (2008). Nursing technicians or auxiliaries were more likely to have been vaccinated, both by univariate and multivariable analysis. When asked about absenteeism, only 10% of the study subjects stated that they would not go to work if they had an influenza-like illness. Those findings suggest that, in non-pandemic periods, influenza control in hospitals requires strategies that combine continuous education with changes in organizational culture.

Circuit board accident - organizational dimension hidden by prescribed safety

This study analyzes an accident in which two maintenance workers suffered severe burns while replacing a circuit breaker panel in a steel mill, following model of analysis and prevention of accidents (MAPA) developed with the objective of enlarging the perimeter of interventions and contributing to deconstruction of blame attribution practices. The study was based on materials produced by a health service team in an in-depth analysis of the accident. The analysis shows that decisions related to system modernization were taken without considering their implications in maintenance scheduling and creating conflicts of priorities and of interests between production and safety; and also reveals that the lack of a systemic perspective in safety management was its principal failure. To explain the accident as merely non-fulfillment of idealized formal safety rules feeds practices of blame attribution supported by alibi norms and inhibits possible prevention. In contrast, accident analyses undertaken in worker health surveillance services show potential to reveal origins of these events incubated in the history of the system ignored in practices guided by the traditional paradigm.

Attitude stabilization of a rigid spacecraft in the geomagnetic field

An analytical method is proposed to study the attitude stability of a triaxial spacecraft moving in a circular Keplerian orbit in the geomagnetic field. The method is developed based on the electrodynamics effect of the influence of the Lorentz force acting on the charged spacecraft's surface. We assume that the rigid spacecraft is equipped with an electrostatic charged protective shield, having an intrinsic magnetic moment. The main elements of this shield are an electrostatic charged cylindrical screen surrounding the protected volume of the spacecraft. The rotational motion of the spacecraft about its centre of mass due to torques from gravitational force, as well Lorentz and magnetic forces is investigated. The equilibrium positions of the spacecraft in the orbital coordinate system are obtained. The necessary and sufficient conditions for the stability of the spacecraft's equilibrium positions are constructed using Lyapunov's direct method. The numerical results have shown that the Lorentz force has a significant influence on the stability of the equilibrium positions, which can affect the attitude stabilization of the spacecraft. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

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.

TIME-OPTIMAL GEOMAGNETIC ATTITUDE MANEUVERS OF AN AXISYMMETRICAL SPINNING SATELLITE

A formulation used to determine the time-optimal geomagnetic attitude maneuvers subject to dynamic and geometric constraints is proposed in this paper. This was obtained by a direct search procedure based on a control function parametrization method, using linear programming to obtain numerical suboptimal solutions by linear perturbation. Due to its characteristics it can be used in small computers and to generate computer programs of general application. The dynamic modeling, the magnetic torque model and the suboptimal control procedure are presented. Simulation runs have verified the feasibility of the formulation thus derived and have shown a notable improvement in performance.

Stability analysis of the attitude of artificial satellites subject to gravity gradient torque

Using a canonical formulation, the stability of the rotational motion of artificial satellites is analyzed considering perturbations due to the gravity gradient torque. Here Andoyer's variables are used to describe the rotational motion. One of the approaches that allow the analysis of the stability of Hamiltonian systems needs the reduction of the Hamiltonian to a normal form. Firstly equilibrium points are found. Using generalized coordinates, the Hamiltonian is expanded in the neighborhood of the linearly stable equilibrium points. In a next step a canonical linear transformation is used to diagonalize the matrix associated to the linear part of the system. The quadratic part of the Hamiltonian is normalized. Based in a Lie-Hori algorithm a semi-analytic process for normalization is applied and the Hamiltonian is normalized up to the fourth order. Once the Hamiltonian is normalized up to order four, the analysis of stability of the equilibrium point is performed using the theorem of Kovalev and Savichenko. This semi-analytical approach was applied considering some data sets of hypothetical satellites. For the considered satellites it was observed few cases of stable motion. This work contributes for space missions where the maintenance of spacecraft attitude stability is required.

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.