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.

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)

Predição analítica do movimento rotacional de satélites estabilizados por rotação

Pós-graduação em Física - FEG

Estudo da estabilidade do movimento rotacional de satélites artificiais com variáveis canônicas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Variáveis canônicas não singulares e o movimento rotacional de satélites artificiais

Pós-graduação em Física - FEG

Influência das propriedades petrográficas na qualidade do polimento de rochas ornamentais

Pós-graduação em Geologia Regional - IGCE

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

Análise da estabilidade do movimento rotacional de satélites artificiais com quatérnions e sob a influência de torques externos

The aim of this work is to analyze the stability of the rotational motion’s artificial satellite using the Routh Hurwitz Algorithm (CRH) and the quaternions to describe the satellite’s attitude. This algorithm allows the investigation of the stability of the motion using the coefficients of the characteristic equation associated with the equation of the rotational motion in the linear form. The equations of the rotational motion are given by the four cinematic equations for the quaternion and the three equations of Euler for the spin velocity’s components. In the Euler equations are included the components of the gravity gradient torque (TGG) and the solar radiation torque (TRS). The TGG is generated by the difference of the Earth gravity force direction and intensity actuating on each satellite mass element and it depends on the mass distribution and the form of the satellite. The TRS is created by changing of the linear momentum, which happens due to the interactions of solar photons with the satellite surface. The equilibrium points are gotten by the equation of rotational motion and the CRH is applied in the linear form of these equations. Simulations are developed for small and medium satellites, but the gotten equilibrium points are not stable by CRH. However, when some of the eigenvalues of the characteristic equation are analyzed, it is found some equilibrium points which can be pointed out as stables for an interval of the time, due to small magnitude of the real part of these eigenvalue

Estudos de acoplamento spin-órbita em dinâmica do sistema solar

Pós-graduação em Física - FEG

g-acceleration of gravity: its measurement from the shape of water by using a computerized rotational system

This paper proposes a different experimental setup compared with the traditional ones, in order to determine the acceleration of gravity, which is carried out by using a fluid at a constant rotation. A computerized rotational system-by using a data acquisition system with specific software, a power amplifier and a rotary motion sensor-is employed in order to evaluate the angular velocity and g. An equation to determine g is inferred from fluid mechanics. For this purpose, the fluid's parabolic shape inside a cylindrical receptacle is considered using a rotational movement.