Abstract
The problem of spherical motions around the center of mass of a single-rotor dynamically symmetrical gyrostat with a spherical cavity, entirely filled with highly viscous fluid, is studied. The motion equations are calculated, stationary motions are found and their stability is studied. Many controls, based on the principle of feedback, are found, stabilizing unstable and stable stationary motions of a gyrostat to asymptotically stable.
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References
Sazonov, V.V., Periodic Motions of a Satellite-Gyrostat Relative to its Center of Mass under the Action of Gravitational Torque, Cosmic Research, 2013, vol. 51, no. 2, pp. 133–146.
Chernous’ko, F.L. On the Motion of a Satellite about Its Centre of Mass under the Action of Gravitational Torques, J. Appl. Math. Mech., 1963, vol. 27, no. 3, pp. 708–722.
Letov, A.M., Dinamika poleta i upravlenie (Flight Dynamics and Control), Moscow: Nauka, 1969.
Rumiantsev, V.V., On the Stability of Motion of Gyrostats, J. Appl. Math. Mech., 1961, vol. 25, no. 1, pp. 9–16.
Krasil’nikov, P.S., Small Plane Oscillations of Satellite in an Weakly Elliptical Orbit, Nelineinaya Dinamika. 2013, vol. 9, no. 4, pp. 671–696.
Orel, O.E. and Ryabov, P.E., Bifurcation Sets in a Problem on Motion of a Rigid Body in Fluid and in the Generalization of this Problem, Regular and Chaotic Dynamics, 1998, vol. 3, no. 2, pp. 82–91.
Hall, C.D and Rand, R.H., Spinup Dynamics of Axial Dual-Spin Spacecraft, Journal of Guidance, Control, and Dynamics, 1994, vol. 17, no. 1, pp. 30–37.
El-Gohary, A., Chaos and Optimal Control of Steady-State Rotation of a Satellite-Gyrostat on a Circular Orbit, Chaos, Solitons & Fractals, 2009, vol. 42, no. 5, pp. 2842–2851.
Bezglasnyi, S.P. and Mysina, O.A., About the Realization of Monoaxial and Triaxial Orientation of a Two-Body System, Vestnik SamGU, 2011, vol. 83, no. 2, pp. 80–90.
Bezglasnyi, S.P. and Khudyakova, M.A., About the Orientation of a Gyrostat with Variable Inertia Moments, Avtomatizatsiya Processov Upravleniya, 2013. vol. 32, no. 2, pp. 22–28.
Chernous’ko, F.L., Dvizhenie tverdogo tela s polost’yami soderzhashchmi vyazkuyu zhidkost’ (Motion of a Rigid Body with Cavities Containing a Viscous Fluid), Moscow: Nauka, 1968.
Moiseev, N.N. and Rumyantsev, V.V., Dinamika tela s polost’yami soderzhashchmi zhidkost’ (Dynamics of Bodies with Fluid-Filled Cavities), Moscow: Nauka, 1965.
Vil’ke, V.G., Motion Evolution of a Symmetric Rigid Body Having a Spherical Cavity Filled with a Viscous Fluid. Vestnik Moskovskogo Universiteta, serie 1, 1993, vol. 48, no. 1, pp. 71–76.
Baranova, E.Yu. and Vil’ke, V.G. Motion Evolution of a Rigid Body with a Fixed Point and an Ellipsoidal Cavity Filled with a Viscous Fluid, Vestnik Moskovskogo Universiteta, serie 1, 2013, vol. 68, no. 1, pp. 44–50.
Akulenko, L.D., Leshchenko, D.D., and Rachinskaya, A.L., Optimal Deceleration of Rotation of a Dynamically Symmetric Body with a Cavity Filled with Viscous Liquid in a Resistive Medium, Journal of Computer and Systems Sciences International, 2010, vol. 49, no. 2, pp. 222–226.
Akulenko, L.D., Zinkevich, Ya.S., Leshchenko, D.D., and Rachinskaya, A.L. Rapid Rotations of a Satellite with a Cavity Filled with Viscous Fluid under the Action of Moment of Gravity and Light Pressure Forces, Cosmic Research, 2011, vol. 49, no. 5, pp. 440–451.
Akulenko, L.D., Leshchenko, D.D., and Rachinskaya, A.L., Optimal Deceleration of Rotation of an Asymmetric Body with a Cavity Filled with Viscous Fluid in a Resistive Medium, Journal of Computer and Systems Sciences International, 2012, vol. 51, no. 1, pp. 38–48.
Alekseev, A.V., Movement of the Satellite-Gyrostat Containing a Cavity with a High-Viscosity Liquid, Izvestiya SNTs RAN, 2007, vol. 9, no. 3, pp. 671–676.
Alekseev, A.V., Bezglasnyi, S.P., and Krasnikov, V.S., Building Stabilizing Control for Stationary Motions of a Gyrostat with a Cavity with Viscous Fluid. Izvestiya SNTs RAN, 2013, vol. 15, no. 6, pp. 563–567.
Aleksandrov, V.V., Boltyanskii, V.G., Lemak, S.S., Parusnikov, N.A., and Tikhomirov, V.M., Optimal’noe upravlenie dvizheniem (Optimal Control of Motion), Moscow: Fizmatlit, 2005.
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Original Russian Text © S.P. Bezglasnyi, published in Izvestiya VUZ. Aviatsionnaya Tekhnika, 2014, No. 4, pp. 7–10.
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Bezglasnyi, S.P. Stabilization of stationary motions of a gyrostat with a cavity filled with viscous fluid. Russ. Aeronaut. 57, 333–338 (2014). https://doi.org/10.3103/S1068799814040023
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DOI: https://doi.org/10.3103/S1068799814040023