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L.D. Akulenko, D.D. Leshchenko, A.L. Rachinskaya, and Yu.S. Shchetinina, "Evolution of Perturbed Rotations of an Asymmetric Gyro in a Gravitational Field and a Resisting Medium," Mech. Solids. 51 (4), 406-414 (2016)
Year 2016 Volume 51 Number 4 Pages 406-414
DOI 10.3103/S002565441604004X
Title Evolution of Perturbed Rotations of an Asymmetric Gyro in a Gravitational Field and a Resisting Medium
Author(s) L.D. Akulenko (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, kumak@ipmnet.ru)
D.D. Leshchenko (Odessa State Academy of Civil Engineering and Architecture, ul. Didrikhsona 4, Odessa, 65029 Ukraine, leshchenko_d@ukr.net)
A.L. Rachinskaya (Mechnikov Odessa National University, ul. Dvoryanskaya 2, Odessa, 65023 Ukraine)
Yu.S. Shchetinina (Mechnikov Odessa National University, ul. Dvoryanskaya 2, Odessa, 65023 Ukraine, powtampik@gmail.com)
Abstract We study the fast rotational motion of a dynamically asymmetric satellite with a spherical cavity filled with a highly viscous liquid about the center of mass under the action of gravitational torque and medium drag torques. The system obtained by averaging over the Euler-Poinsot motion and by using a modified averaging method is analyzed. An analytic study and numerical analysis are carried out.
Keywords satellite, gravitational torque, medium resistance, cavity filled with a viscous liquid, averaging
References
1.  V. V. Beletskii, Artificial Satellite Motion about Its Center of Mass (Nauka, Moscow, 1965) [in Russian].
2.  F. L. Chernous'ko, "On the Motion of a Satellite about Its Center of Mass under the Action of Gravitational Torques," Prikl. Mat. Mekh. 27 (3), 474-483 (1963) [J. Appl. Math. Mech. (Engl. Transl.) 27 (3), 708-722 (1963)].
3.  V. V. Beletskii, Satellite Motion about the Center of Mass in Gravitational Field (Izd-vo MGU, Moscow, 1975) [in Russian].
4.  F. L. Chernous'ko, "Motion of a Rigid Body with Cavities Filled with Viscous Fluid at Small Reynolds Numbers," Zh. Vychisl. Mat. Mat. Fiz. 5 (6), 1049-1070 (1965) [U.S.S.R. Comput. Math. Math. Phys. (Engl. Transl.) 5 (6), 99-127 (1965)].
5.  V. N. Koshlyakov, Problems of Solid Mechanics and Applied Theory of Gyros: Analytic Method (Nauka, Moscow, 1985) [in Russian].
6.  L. D. Akulenko, D. D. Leshchenko, and F. L. Chernous'ko, "Fast Motion of a Heavy Rigit Body about a Fixed Point in a Resistive Medium," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 3, 5-13 (1982) [Mech. Solids (Engl. Transl.) 17 (3), 1-8 (1982)].
7.  M. Iñarrea and V. Lanchares, "Chaotic Pitch Motion of an Asymmetric Nonrigid Spacecraft with Viscous Drag in a Circular Orbit," Int. J. Non-Lin. Mech. 41, 86-100 (2006).
8.  L. D. Akulenko, D. D. Leshchenko, and A. L. Rachinskaya, "Evolution of the Satellite Fast Rotation Due to the Gravitational Torque in a Resisting Medium," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 13-26 (2008) [Mech. Solids (Engl. Transl.) 43 (2), 173-184 (2008)].
9.  E. P. Smirnova, "Stabilization of Free Rotation of an Asymmetric Top with Cavities Completely Filled with a Fluid," Prikl. Mat. Mekh. 38 (6), 980-985 (1974) [J. Appl. Math. Mech. (Engl. Transl.) 38 (6), 931-935 (1974)].
10.  E. P. Osipov and R. S. Sulikashvili, "On Oscillations of a Rigid Body with a Cavity Completely Filled with a Viscous Liquid in an Ellipsoidal Orbit," Trudy Tbilis. Matem. Inst. Akad. Nauk GSSR 58, 175-186 (1978).
11.  L. D. Akulenko and D. D. Leshchenko, "Rapid Rotation of a Heavy Gyrostat about a Fixed Point in a Resisting Medium," Prikl. Mekh. 18 (7), 102-107 (1982) [Int. Appl. Mech. (Engl. Transl.) 18 (7), 660-665 (1982)].
12.  V. V. Sidorenko, "Evolution of the Rotational Motion of a Planet with a Liquid Core," Astron. Vestnik 27 (2), 119-127 (1993) [Solar Syst. Res. (Engl. Transl.) 27 (2), 201-208 (1993)].
13.  L. D. Akulenko, D. D. Leshchenko, and A. L. Rachinskaya, "Evolution of Rotations of a Satellite with a Cavity Filled with a Viscous Liquid," Mekh. Tverd. Tela, No. 37, 126-139 (2007).
14.  D. D. Leshchenko and S. G. Suksova, "On the Motion of an Asymmetric Gyro in a Resisting Medium,' J. Intern. Federation of Nonlinear Analysts - Acad. Nonlinear Sci. "Problemy Nelineinogo Analiza v Inzhenernykh Sistemakh" 9 (2)(18), 83-89 (2003).
15.  E. Yu. Baranova and V. G. Vilke, "Evolution of Motion of a Rigid Body with a Fixed Point and an Ellipsoidal Cavity Filled with a Viscous Fluid," Vestnik Moskov. Univ. Ser. I Mat. Mekh., No. 1, 44-50 (2013) [Moscow Univ. Mech. Bull. (Engl. Transl.) 68 (1), 15-20 (2013)].
16.  L. D. Akulenko, Ya. S. Zinkevich, D. D. Leshchenko, and A. L. Rachinskaya, "Rapid Rotations of a Satellite with a Cavity Filled with a Viscous Fluid under the Action of Moments of Gravity and Light Pressure Forces," Kosmich. Issled. 49 (5), 453-463 (2011) [Cosmic Res. (Engl. Transl.) 49 (5), 440-451 (2011)].
17.  D. D. Leshchenko, A. L. Rachinskaya, and Yu. S. Shchetinina, "Evolution of Rotations of a Symmetric Gyro in a Gravity Field and in a Resisting Medium," Makhanika Tverd. Tela, No. 42, 93-102 (2012).
18.  L. D. Akulenko, D. D. Leshchenko, A. L. Rachinskaya, and Ya. S. Zinkevich, Perturbed and Controlled Rotations of a Rigid Body (Mechnikov Odessa Nation. Univ., Odessa, 2013) [in Russian].
19.  V. M. Volosov and B. I. Morgunov, Averaging Method in the Theory of Nonlinear Oscillatory Systems (Izdat. MGU, Moscow, 1971) [in Russian].
20.  L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 1: Mechanics (Nauka, Moscow, 1973; Pergamon Press, Oxford, 1976).
21.  L. D. Akulenko, "Higher-Order Averaging Schemes in Systems with Fast and Slow Phases," Prikl. Mat. Mekh. 66 (2), 165-176 (2002) [J. Appl. Math. Mech. (Engl. Transl.) 66 (2), 153-163 (2002)].
22.  I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Nauka, Moscow, 1971) [in Russian].
23.  E. Kamke, Reference Book in Ordinary Differential Equations (Van Nostrand, New York, 1960; Nauka, Moscow, 1971).
24.  V. Volterra, Mathematical Theory of the Struggle for Existence (Nauka, Moscow, 1976) [in Russian].
Received 25 June 2014
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