Abstract—
The paper presents the reconstruction results of rotational motion of the AIST-2D small spacecraft by onboard measurements of vectors of angular velocity and the strength of Earth’s magnetic field obtained in summer 2016. The reconstruction method is based on the reconstruction of kinematic equations of the rotational motion of a solid body. According to the method, measurement data of both types collected on a certain time interval are processed together. Measurements of the angular velocity are interpolated by piecewise-linear functions, which are replaced in kinematic differential equations for a quaternion that defines the transformation from the satellite instrument coordinate system to the inertial coordinate system. The obtained equations represent the kinematic model of the rotational motion of a satellite. A solution to these equations that approximates the actual motion is derived from the condition of the best (in the sense of the least squares method) match between the measurement data of the strength vector of Earth’s magnetic field and its calculated values. The initial conditions of the approximating solution, constant bias in angular velocity measurements, and angles specifying the matrices of transformation from magnetometer intrinsic coordinate systems to the instrument coordinate system of the satellite (measurements of the angular velocity are specified in it) are refined. The described method makes it possible to reconstruct the actual rotational motion of a satellite using one solution of kinematic equations over time intervals longer than 10 h.
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REFERENCES
Abrashkin, V.I., Voronov, K.E., Piyakov, I.V., Puzin, Yu.Ya., Sazonov, V.V., Semkin, N.D., Chebukov, S.Yu., Determining the rotational motion of the Bion M-1 satellite with the GRAVITON instrument, Cosmic Res., 2015, vol. 53, no. 4, pp. 286–299.
Abrashkin, V.I., Voronov, K.E., Piyakov, I.V., Puzin, Yu.Ya., Sazonov, V.V., Semkin, N.D., and Chebukov, S.Yu., Rotational motion of Foton M-4, Cosmic Res., 2016, vol. 54, no. 4, pp. 296–302.
Abrashkin, V.I., Voronov, K.E., Piyakov, I.V., Puzin, Yu.Ya., Sazonov, V.V., Semkin, N.D., and Chebukov, S.Yu., A simplified technique for determining the rotational motion of a satellite based on the onboard measurements of the angular velocity and magnetic field of the Earth, Cosmic Res., 2016, vol. 54, no. 5, pp. 375–387.
Abrashkin, V.I., Bogoyavlenskii, N.L., Voronov, K.E., Kazakova, A.E., Puzin, Yu.Ya., Sazonov, V.V., Semkin, N.D., and Chebukov, S.Yu., Uncontrolled motion of the Foton M-2 satellite and quasistatic microaccelerations on its board, Cosmic Res., 2007, vol. 45, no. 5, pp. 424–443.
Abrashkin, V.I., Voronov, K.E., Piyakov, A.V., Puzin, Yu.Ya., Sazonov, V.V., Semkin, N.D., Filippov, A.S., and Chebukov, S.Yu., Uncontrolled attitude motion of the small satellite AIST, Cosmic Res., 2015, vol. 53, no. 5, pp. 360–373.
Abrashkin, V.I., Voronov, K.E., Piyakov, A.V., Puzin, Yu.Ya., Sazonov, V.V., Semkin, N.D., Filippov, A.S., and Chebukov, S.Yu., Uncontrolled rotational motion of the Aist small spacecraft prototype, Cosmic Res., 2017, vol. 55, no. 2, pp. 128–141.
Hoots, F.R. and Roehrich, R.L., Models for Propagation of NORAD Element Sets, Aerospace Defense Command, United States Air Force, 1988, Spacetrack Report no. 3.
Gill, P.E., Murray, W., and Wright, M.H., Practical Optimization, London: Academic, 1981; Moscow: Mir, 1985.
Pankratova, V.A. and Sazonov, V.V., Checking the consistency of measurement data from magnetometers onboard an artificial satellite of the Earth, Preprint of Keldysh Institute of Applied Mathematics, Russ. Acad. Sci., Moscow, 2010, no. 42.
Abrashkin, V.I., Voronov, K.E., Dorofeev, A.S., Piyakov, A.V., Puzin, Yu.Ya., Sazonov, V.V., Semkin, N.D., Filippov, A.S., and Chebukov, S.Yu., Determination of the rotational motion of the small satellite Aist-2D according to data from the KMU-1 micro-acceleration dumper, Preprint of Keldysh Institute of Applied Mathematics, Russ. Acad. Sci., Moscow, 2017, no. 57.
ACKNOWLEDGMENTS
This work was supported by the Russian Foundation for Basic Research, project no. 17-01-00143.
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Abrashkin, V.I., Voronov, K.E., Dorofeev, A.S. et al. Detection of the Rotational Motion of the AIST-2D Small Spacecraft by Magnetic Measurements. Cosmic Res 57, 48–60 (2019). https://doi.org/10.1134/S0010952519010015
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DOI: https://doi.org/10.1134/S0010952519010015