Spin‐Stabilized Spacecrafts: Analytical Attitude Propagation Using Magnetic Torques

Abstract

An analytical approach for spin-stabilized satellites attitude propagation is presented, considering the influence of the residual magnetic torque and eddy currents torque. It is assumed two approaches to examine the influence of external torques acting during the motion of the satellite, with the Earth's magnetic field described by the quadripole model. In the first approach is included only the residual magnetic torque in the motion equations, with the satellites in circular or elliptical orbit. In the second approach only the eddy currents torque is analyzed, with the satellite in circular orbit. The inclusion of these torques on the dynamic equations of spin stabilized satellites yields the conditions to derive an analytical solution. The solutions show that residual torque does not affect the spin velocity magnitude, contributing only for the precession and the drift of the spacecraft's spin axis and the eddy currents torque causes an exponential decay of the angular velocity magnitude. Numerical simulations performed with data of the Brazilian Satellites (SCD1 and SCD2) show the period that analytical solution can be used to the attitude propagation, within the dispersion range of the attitude determination system performance of Satellite Control Center of Brazil National Research Institute.

Spin stabilized satellite's attitude propagation with quaternions

“…It is known (Garcia et al (2009) and Zanardi et al (2005)) that the eddy currents produce a torque which causes the precession in the spin axis and causes an exponential decay of the spin rate. If ���⃗ is the spacecraft's angular velocity vector and p is a constant coefficient which depends on the spacecraft geometry and conductivity, this torque is given by:…”

“…The spacecraft's magnetic moment is usually the dominant source between the disturbances torques (Vilhena de Moraes, 1994). If m  is the magnetic moment of the spacecraft and B  is the geocentric magnetic flux density, the residual magnetic torques is given by Garcia et al (2009), Zanardi et al (2005 and Zanardi and Real (2003):…”

“…In this case, the spacecraft's angular velocity vector and the satellite magnetic moment are along the z-axis and the residual magnetic torque and the induced eddy currents can the expressed in the satellite fixed system by (Garcia et al, 2009):…”

Efeitos dos torques magnéticos no movimento rotacional de satélites estabilizados por rotação

“…Saliente se que o modelo de vetor de dipolo mostrou-se bastante adequado na análise realizada em [1], [2], [8] e [9]. A análise aqui realizada, utilizando apenas os torques magnéticos, se justifica por estes serem os torques de maior magnitude para as características orbitais e geométricas do SCD1.…”

“…A abordagem aqui apresentada corresponde a um refinamento nas soluções analíticas de Garcia [1], Garcia et al [2], Quirelli [8], Quirelli et al [9] e Pereira [5], diferenciando da abordagem realizada por Pereira [6] e Zanardi e Pereira [12] por utilizar modelos distintos para o campo geomagnético e por avaliar os torques a cada período orbital, e não a cada inicio do dia como assumido em [6] e [12] nas aplicações para o SCD1.…”