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 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.

Consumer attitude towards purchasing intent for ready to drink orange juice and nectar

Purpose: The purpose of this paper was to evaluate the impact of some labeling aspects on the consumer intent to purchase ready to drink orange juice and nectar. Design/methodology/approach: The influence of label information on the consumer intent to purchase was evaluated by conjoint analysis using a convenience sample (n=149). A factorial design with four characteristics, price, brand, information about the product and kind of beverage, was used. Three levels were established for brand and product information, and two for price and kind of beverage. Findings: Low price, product information and market leading brand had positive impact. No preservatives/natural was the information that most influenced consumer's purchase intent. The ideal label showed the leading brand, low price and information no preservatives/natural. These results could be useful for strategic planning of consumer instruction and have important implications for Brazilian orange juice manufactures. Originality/value: Although the most widely consumed beverages in Brazil are ready to drink orange juice and nectar, it was unexpected that consumers did not know the differences between them and that kind of beverage was not an important factor for the purchase decision. © Emerald Group Publishing Limited.

Attitude of Brazilian veterinarians in the recognition and treatment of pain in horses and cattle

Objective: The objective of this study was to assess the use of analgesics, describe the attitudes of Brazilian veterinarians towards pain relief in horses and cattle and evaluate the differences due to gender, year of graduation and type of practice. Study design: Prospective survey. Methods: Questionnaires were sent to 1000 large animal veterinarians by mail, internet and delivered in person during national meetings. The survey investigated the attitudes of Brazilian veterinarians to the recognition and treatment of pain in large animals and consisted of sections asking about demographic data, use of analgesic drugs, attitudes to pain relief and to the assessment of pain. Descriptive statistics were used to analyze frequencies. Simple post hoc comparisons were performed using the chi-square test. Results: Eight hundred questionnaires were collected, but 87 were discarded because they were incomplete or blank. The opioid of choice for use in large animals was butorphanol (43.4%) followed by tramadol (39%). Flunixin (83.2%) and ketoprofen (67.6%) were the most frequently used NSAIDs by Brazilian veterinarians. Respondents indicated that horses received preoperative analgesics for laparotomy more frequently (72.9%) than cattle (58.5%). The most frequently administered preoperative drugs for laparotomy in horses were flunixin (38.4%) and xylazine (23.6%), whereas the preoperative drugs for the same surgical procedure in cattle were xylazine (31.8%) and the local administration of lidocaine (48%). Fracture repair was considered the most painful surgical procedure for both species. Most veterinarians (84.1%) believed that their knowledge in this area was not adequate. Conclusions and clinical relevance: Although these Brazilian veterinarians thought that their knowledge on recognition and treatment of pain was not adequate, the use of analgesic in large animals was similar in Brazil to that reported in other countries. © 2013 Association of Veterinary Anaesthetists and the American College of Veterinary Anesthesia and Analgesia.

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.

Perception and Attitude About Systemic Health and Periodontal Disease Among Dentistry Undergraduates

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A note on the hypercomplex riemann-cauchy like relations for quaternions and laplace equations

In this Note it is worked out a new set of Laplace-Like equations for quaternions through Riemann-Cauchy hypercomplex relations otained earlier [1]. As in the theory of functions of a complex variable, it is expected that this new set of Laplace-Like equations might be applied to a large number of Physical problems, providing new insights in the Classical Fields Theory.

Fourier series for quaternions and the square of the error theorem

In this paper we introduce a type of Hypercomplex Fourier Series based on Quaternions, and discuss on a Hypercomplex version of the Square of the Error Theorem. Since their discovery by Hamilton (Sinegre [1]), quaternions have provided beautifully insights either on the structure of different areas of Mathematics or in the connections of Mathematics with other fields. For instance: I) Pauli spin matrices used in Physics can be easily explained through quaternions analysis (Lan [2]); II) Fundamental theorem of Algebra (Eilenberg [3]), which asserts that the polynomial analysis in quaternions maps into itself the four dimensional sphere of all real quaternions, with the point infinity added, and the degree of this map is n. Motivated on earlier works by two of us on Power Series (Pendeza et al. [4]), and in a recent paper on Liouville’s Theorem (Borges and Mar˜o [5]), we obtain an Hypercomplex version of the Fourier Series, which hopefully can be used for the treatment of hypergeometric partial differential equations such as the dumped harmonic oscillation.

Fault detection, diagnosis and active fault tolerant control for a satellite attitude control system

Modern control systems are becoming more and more complex and control algorithms more and more sophisticated. Consequently, Fault Detection and Diagnosis (FDD) and Fault Tolerant Control (FTC) have gained central importance over the past decades, due to the increasing requirements of availability, cost efficiency, reliability and operating safety. This thesis deals with the FDD and FTC problems in a spacecraft Attitude Determination and Control System (ADCS). Firstly, the detailed nonlinear models of the spacecraft attitude dynamics and kinematics are described, along with the dynamic models of the actuators and main external disturbance sources. The considered ADCS is composed of an array of four redundant reaction wheels. A set of sensors provides satellite angular velocity, attitude and flywheel spin rate information. Then, general overviews of the Fault Detection and Isolation (FDI), Fault Estimation (FE) and Fault Tolerant Control (FTC) problems are presented, and the design and implementation of a novel diagnosis system is described. The system consists of a FDI module composed of properly organized model-based residual filters, exploiting the available input and output information for the detection and localization of an occurred fault. A proper fault mapping procedure and the nonlinear geometric approach are exploited to design residual filters explicitly decoupled from the external aerodynamic disturbance and sensitive to specific sets of faults. The subsequent use of suitable adaptive FE algorithms, based on the exploitation of radial basis function neural networks, allows to obtain accurate fault estimations. Finally, this estimation is actively exploited in a FTC scheme to achieve a suitable fault accommodation and guarantee the desired control performances. A standard sliding mode controller is implemented for attitude stabilization and control. Several simulation results are given to highlight the performances of the overall designed system in case of different types of faults affecting the ADCS actuators and sensors.

Magnetic actuators for nanosatellite attitude control

The research and the activities presented in the following thesis report have been led at the California Polytechnic State University (US) under the supervision of Prof. Jordi Puig Suari. The objective of the research has been the study of magnetic actuators for nanosatellite attitude control, called magnetorquer. Theese actuators are generally divided in three different kinds: air core torquer, embedded coil and torquerod. In a first phase of the activity, each technology has been analyzed, defining advantages and disadvantages, determining manufacturing procedures and creating mathematical model and designing equation. Dimensioning tools have been then implemented in numerical software to create an instrument that permits to determine the optimal configuration for defined requirements and constraints. In a second phase of the activities the models created have been validated exploiting prototypes and proper instruments for measurements. The instruments and the material exploited for experiments and prototyping have been provided by the PolySat and CubeSat laboratories. The results obtained led to the definition of a complete designing tool and procedure for nanosatellite magnetic actuators, introducing a cost analysis for each kind of solution. The models and the tools have been maintained fully parametric in order to offer a universal re-scalable instrument for satellite of different dimension class.