Study of Stability of Rotational Motion of Spacecraft with Canonical Variables

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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 and semi-analytical analysis of an artificial satellite's rotational motion

The rotational motion of an artificial satellite is studied by considering torques produced by gravity gradient and direct solar radiation pressure. A satellite of circular cylinder shape is considered here, and Andoyers variables are used to describe the rotational motion. Expressions for direct solar radiation torque are derived. When the earth's shadow is not considered, an analytical solution is obtained using Lagrange's method of variation of parameters. A semi-analytical procedure is proposed to predict the satellite's attitude under the influence of the earth's shadow. The analytical solution shows that angular variables are linear and periodic functions of time while their conjugates suffer only periodic variations. When compared, numerical and analytical solutions have a good agreement during the time range considered.

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.

Sobre a dinâmica de rotação de um planeta através de um sistema médio

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Iniciação ao estudo da dinâmica de rotação de um satélite em variáves de Andoyer

The dynamics of the rotation of a satellite is an old and classical problem, specially in the Euler formalism. However, with these variables, even in torque free motion problem, the integrability of the system is far from trivial, mainly when the three moments of the inertia are not equal. Another disadvantage occurs when the inclinations between some plans are null or close to zero, so the nodes become undetermined. In this work, we propose the use of modern Andoyer's variables. These are a set of canonical variables and therefore some significant advantages can be obtained when dealing with perturbation methods. On other the hand, the integrability of the torque free motion becomes very clear, as the system is reduced to a problem of one degree of freedom. The elimination of the singularities mentioned above, can be solved very easily, with Pincaré-type variables. In this work we give the background concepts of the Andoyer's variables and the disturbing potential is obtained for the rotational dynamics of a satellite perturbed by a planet. In the case when A = B (moments of inertia) and due to the current variables, the averaged system is trivially obtained through very simple integrations

Cross-correlations between weather variables in Australia

The information on climate variations is essential for the research of many subjects, such as the performance of buildings and agricultural production. However, recorded meteorological data are often incomplete. There may be a limited number of locations recorded, while the number of recorded climatic variables and the time intervals can also be inadequate. Therefore, the hourly data of key weather parameters as required by many building simulation programmes are typically not readily available. To overcome this gap in measured information, several empirical methods and weather data generators have been developed. They generally employ statistical analysis techniques to model the variations of individual climatic variables, while the possible interactions between different weather parameters are largely ignored. Based on a statistical analysis of 10 years historical hourly climatic data over all capital cities in Australia, this paper reports on the finding of strong correlations between several specific weather variables. It is found that there are strong linear correlations between the hourly variations of global solar irradiation (GSI) and dry bulb temperature (DBT), and between the hourly variations of DBT and relative humidity (RH). With an increase in GSI, DBT would generally increase, while the RH tends to decrease. However, no such a clear correlation can be found between the DBT and atmospheric pressure (P), and between the DBT and wind speed. These findings will be useful for the research and practice in building performance simulation.

Identification of critical input variables for risk-based cost estimates for road maintenance and rehabilitation

An estimation of costs for maintenance and rehabilitation is subject to variation due to the uncertainties of input parameters. This paper presents the results of an analysis to identify input parameters that affect the prediction of variation in road deterioration. Road data obtained from 1688 km of a national highway located in the tropical northeast of Queensland in Australia were used in the analysis. Data were analysed using a probability-based method, the Monte Carlo simulation technique and HDM-4’s roughness prediction model. The results of the analysis indicated that among the input parameters the variability of pavement strength, rut depth, annual equivalent axle load and initial roughness affected the variability of the predicted roughness. The second part of the paper presents an analysis to assess the variation in cost estimates due to the variability of the overall identified critical input parameters.

Using Trauma Injury Severity Score (TRISS) variables to predict length of hospital stay following trauma in New Zealand

Aim – To develop and assess the predictive capabilities of a statistical model that relates routinely collected Trauma Injury Severity Score (TRISS) variables to length of hospital stay (LOS) in survivors of traumatic injury. Method – Retrospective cohort study of adults who sustained a serious traumatic injury, and who survived until discharge from Auckland City, Middlemore, Waikato, or North Shore Hospitals between 2002 and 2006. Cubic-root transformed LOS was analysed using two-level mixed-effects regression models. Results – 1498 eligible patients were identified, 1446 (97%) injured from a blunt mechanism and 52 (3%) from a penetrating mechanism. For blunt mechanism trauma, 1096 (76%) were male, average age was 37 years (range: 15-94 years), and LOS and TRISS score information was available for 1362 patients. Spearman’s correlation and the median absolute prediction error between LOS and the original TRISS model was ρ=0.31 and 10.8 days, respectively, and between LOS and the final multivariable two-level mixed-effects regression model was ρ=0.38 and 6.0 days, respectively. Insufficient data were available for the analysis of penetrating mechanism models. Conclusions – Neither the original TRISS model nor the refined model has sufficient ability to accurately or reliably predict LOS. Additional predictor variables for LOS and other indicators for morbidity need to be considered.

A comparative study of manufacturing practices and performance variables

The reported study was conducted to compare and contrast current manufacturing practices between two countries, Australia and Malaysia, and identify the practices that significantly influence their manufacturing performances. The results are based on data collected from surveys using a standard questionnaire in both countries. Evidence indicates that product quality and reliability is the main competitive factor for manufacturers. Maintaining a supplier rating system and regularly updating it with field failure and warranty data and making use of product data management are found to be effective manufacturing practices. In terms of the investigated manufacturing performance, Australian manufacturers are marginally ahead of their Malaysian counterparts. However, Malaysian manufacturers came out ahead on most dimensions of advanced quality and manufacturing practices, particularly in the adoption of product data management, effective supply chains and relationships with suppliers and customers.