# Analysis of analytical attitude propagators for spin-stabilized satellites

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## Abstract

In this paper, analytical attitude propagators for spin-stabilized satellites are analyzed. For this purpose, external torques are introduced in the motion equations such as solar radiation pressure torque, aerodynamic torque, gravity gradient torque, and magnetic residual and eddy current torques. For the magnetic torques, it used both the dipole and quadripole Earth’s magnetic field models. The obtained analytical solution is applied and compared with actual data for Brazilian data collection satellites SCD1 and SCD2. The results, when a daily data update is applied, based on the INPE-Brazilian Institute for Space Research supplied data, show a good agreement of all involved parameters with the actual deviations in the parameter values within the precision required for the satellite mission. This permits to conclude that the used theory is suitable for the studied problem. Thus, the propagators presented in this work can be applied to predict the rotational motion of spin-stabilized artificial satellites, particularly for SCD1 and SCD2 satellites over the considered time period.

## Keywords

Analytical propagators Spin-stabilized satellites Environmental torques## Mathematics Subject Classification

34A34## Notes

### Acknowledgements

This present work was supported by CAPES-PVNS and CNPq (Process no. 421672/2016-1).

## References

- Carrara V (2014) Environmental disturbance models for satellites. In: Proceedings of XXXV Iberian Latin America congress on computational methods in engineering, CILANCE2014Google Scholar
- Carrara V (2015) An open source satellite attitude and orbit simulator for Matlab. In: Proceedings of XVII international symposium on dynamic problems of mechanicsGoogle Scholar
- da Fonseca IM, Bainum PM (2006) The Brazilian satellite program—a survey. Adv Astron Sci 122:505–532Google Scholar
- de Moraes RV, Zanardi MC (1999) Analytical and semi-analytical analysis an artificial satellite’s rotational motion. Cel Mech Dyn Astr 75:227–250CrossRefGoogle Scholar
- Garcia RV, Zanardi MC, Kuga HK (2009) Spin-stabilized spacecrafts: analytical attitude propagation using magnetic torques. Math Prob Eng 2009:1–19CrossRefGoogle Scholar
- Hara M (1973) Effects of magnetic and gravitational torques in spinning satellite attitude. AIAA J II(12):1737–1742CrossRefGoogle Scholar
- Kuga HK, Ferreira LDD, Guedes UTV (1987) Simulação de atitude e de manobras para o satélite brasileiro estabilizado por rotação. In: Anais do IX COBEM, pp 911–914Google Scholar
- Kuga HK, Orlando V, Lopes RVF (1999) Flight dynamics operations during leop for the INPE’s second environmental data collecting satellite SCD2. Rev Bras de Ciênc Mec 21:339–344Google Scholar
- Lopes RVF, Rao KR (1994) SCD-1 Attitude follow-up: from initial idea to final facts. In: Proceedings of II Brazilian symposium on aerospace technology VvII, pp 281–284Google Scholar
- Lopes RVF, Fabri SM, Ferreira LDD (1997) Attitude determination for spin stabilized satellites from GPS interferometry. Adv Astron Sci 95(2):783–802Google Scholar
- Maciejewski AJ, Przybylska M (2003) Non-integrability of the problem of a rigid satellite in gravitational and magnetic fields. Cel Mech Dyn Astron 87(4):317–351MathSciNetCrossRefGoogle Scholar
- Motta GB, Zanardi MC (2014) Influence of the external torques in the angle between the spin axis and the Sun direction for spin stabilized satellite. J Phys: Conf Ser 641:012022Google Scholar
- Motta GB, Carvalho MV, Zanardi MC (2013) Analytical prediction of the spin stabilized satellite’s attitude using the solar radiation torque. J Phys Conf Ser V 465:012009CrossRefGoogle Scholar
- Orlando V, Lopes RVF, Kuga HK (1997) INPE’s flight dynamics team experience through four years of SCD1 in-orbit operation: main issues, improvements and trends. In: Proceedings of 12th international symposium on space flight dynamics, pp 433–437Google Scholar
- Orlando V, Kuga HK, Guedes UTV (1998) Flight dynamics LEOP and routine operations for SCD2, the INPE’ second environmental data collecting satellite. Adv Astron Sci 100:1003–1013Google Scholar
- Rao KR, Lopes RVF (1995) Satellite Attitude Follow-up: a first-hand experience with the first Brazilian Satellite SCD-1. In: Proceedings of international symposium on space dynamics, pp 777–783Google Scholar
- Sarychev VA, Guerman A, Paglione P (2003) Infuence of constant torque on equilibria of satellite in circular orbit. Celest Mech Dyn Astron 87(3):219–239CrossRefGoogle Scholar
- Sehnal L, Pospísilová L (1988) Thermospheric model TD88. Preprint no. 67 of the Astronomical Institute of Czechoslovakian Academy of SciencesGoogle Scholar
- Shivastava SK, Modi VJ (1993) Satellite attitude dynamics and control in the presence of environmental torques—a brief survey. AIAA J 6(6):461–471Google Scholar
- Thomas LC, Cappelari JO (1964) Attitude determination and prediction of spin stabilized satellites. Bell Syst Tech J 43:1654CrossRefGoogle Scholar
- Venkataraman NS, Carrara V (1983) The modelling of forces and torques on near Earth satellites. In: Proceedings of VII Congresso Brasileiro de Engenharia Mecânica—COBEM 83, vol B, pp 23–133Google Scholar
- Wertz JR (1978) Spacecraft attitude determination and control. Reidel, LondonCrossRefGoogle Scholar
- Yu EY (1963) Spin decay, spin-precession damping, and spin-axis drift of the telstar satellite. Bell Syst Tech J 42:2169–2193CrossRefGoogle Scholar
- Zanardi MC, Quirelli IMP, Kuga HK (2003) Analytical attitude propagation of spin stabilized Earth artificial satellites. In: Proceedings of 17th international symposium on space flight dynamics.Google Scholar
- Zanardi MC, Quirelli IMP, Kuga HK (2005) Analytical attitude prediction of spin stabilized spacecrafts perturbed by magnetic residual torques. Adv Sp Res 36:460–465CrossRefGoogle Scholar
- Zanardi MC, Pereira A, Chiaradia JE (2011) Spin stabilizes satellite’s attitude analytical prediction. In: Proceedings of 22th international symposium on space flight dynamics, pp 1–14. http://issfd.org. Accessed Mar 2017
- Zanardi MC, Orlando V, Motta GB, Pelosi T, Silva WR (2016) Numerical and analytical approach for the spin-stabilized satellite attitude propagation. Comp Appl Math 1:1–13MathSciNetzbMATHGoogle Scholar