Abstract
The subject of this book is the investigation of perturbed motions of a rigid body about its center of mass under the action of torques of various physical nature. If the body is not acted upon by the internal or external torques, then it performs a certain motion which is called unperturbed. As an unperturbed motion, one usually considers the motion in the case of Euler or Lagrange. In real conditions, the body is acted upon by the perturbation moments of internal or external forces, in particular, gravitation forces, the forces of the medium resistance and the internal dissipative forces.
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References
Bogolubov, N.N., Mitropolsky, Y.A.: Asymptotic Methods in the Theory of Nonlinear Oscillations. Gordon and Breach Science Publishers, New York (1961)
Volosov, V.M., Morgunov, B.I.: The Averaging Method in the Theory of Non-linear Oscillatory Systems. Moscow State Univ., Moscow (1971) in Russian
Mitropolsky, Yu.A.: The Method of Averaging in Nonlinear Mechanics. Naukova Dumka, Kiev (1971) in Russian
Demin, V.G., Konkina, L.I.: New Methods in Dynamics of a Rigid Body. Ilim, Frunze (1989) in Russian
Bulgakov, B.V.: Applied Theory of Gyroscopes, 3rd edn. Moscow State Univ., Moscow (1976) in Russian
Beletsky, V.V.: Motion of an Artificial Satellite about its Center of Mass. Israel Program for Scientific Translation, Jerusalem (1966)
Beletsky, V.V.: Spacecraft Attitude Motion in Gravity Field. Moscow State Univ., Moscow (1975) in Russian
Chernousko, F.L.: On the motion of a satellite about its center of mass under the action of gravitational moments. J. Appl. Math. Mech. 27(3), 708–722 (1963)
Moiseev, N.N.: Asymptotic Methods of Nonlinear Mechanics. Nauka, Moscow (1981) in Russian
Akulenko, L.D.: Asymptotic Methods of Optimal Control. Nauka, Moscow (1987) in Russian
Akulenko, L.D.: Problems and Methods of Optimal Control. Kluwer, Dordrecht (1994)
Akulenko, L.D.: Higher-order averaging schemes in systems with fast and slow phases. J. Appl. Math. Mech. 66(2), 153–163 (2002)
Arnold, V.I., Kozlov, V.V., Neishtadt, A.I.: Mathematical Aspects of Classical and Celestial Mechanics. Springer, Berlin (2007)
Neishtadt, A.I.: On the separation of motions in the systems with the fast-rotating phase. Prikl. Mat. Mekh. 48(2), 197–204 (1984) in Russian
Akulenko, L.D.: Higher-order averaging schemes in the theory of non-linear oscillations. Prikl. Mat. Mekh. 65(5), 843–853 (2001) in Russian
Chernousko, F.L.: Motion of a rigid body with cavities filled with viscous fluid at small Reynolds number. USSR Comput. Math. Math. Phys. 5(6), 99–127 (1965)
Chernousko, F.L.: Motion of a Rigid Body with Viscous-Fluid-Filled Cavities. Computing Center AN SSSR, Moscow (1968) in Russian
Chernousko, F.L.: The Movement of a Rigid Body with Cavities Containing a Viscous Fluid. NASA, Washington (1972)
Lamy, P., Burns, J.: Geometrical approach to torque free motion of a rigid body having internal energy dissipation. Am. J. Phys. 40(3), 441–445 (1972)
Klimov, D.M., Kosmodem’yanskaya, G.V., Chernousko, F.L.: Motion of a gyroscope with contactless suspension. Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela. 2, 3–8 (1972) in Russian
Appel, P.: Traite de Mechanique Rationnelle. Gauthier – Villars, Paris (1953)
Landau, L.D., Lifshitz, E.M.: Course of Theoretical Physics, Mechanics, vol. 1. Pergamon Press, Oxford (1976)
Arnold, V.I.: Geometrical Methods in the Theory of Ordinary Differential Equations. Springer, London (2012)
Leshchenko, D.D., Shamaev, A.S.: Perturbed rotational motions of a rigid body that are close to regular precession in the Lagrange case. Mech. Solids. 22(6), 6–15 (1987)
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Chernousko, F.L., Akulenko, L.D., Leshchenko, D.D. (2017). Equations of Perturbed Motion of a Rigid Body About Its Center of Mass. In: Evolution of Motions of a Rigid Body About its Center of Mass. Springer, Cham. https://doi.org/10.1007/978-3-319-53928-7_4
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DOI: https://doi.org/10.1007/978-3-319-53928-7_4
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