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Equations of Perturbed Motion of a Rigid Body About Its Center of Mass

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Book cover Evolution of Motions of a Rigid Body About its Center of Mass

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

  1. Bogolubov, N.N., Mitropolsky, Y.A.: Asymptotic Methods in the Theory of Nonlinear Oscillations. Gordon and Breach Science Publishers, New York (1961)

    Google Scholar 

  2. Volosov, V.M., Morgunov, B.I.: The Averaging Method in the Theory of Non-linear Oscillatory Systems. Moscow State Univ., Moscow (1971) in Russian

    Google Scholar 

  3. Mitropolsky, Yu.A.: The Method of Averaging in Nonlinear Mechanics. Naukova Dumka, Kiev (1971) in Russian

    Google Scholar 

  4. Demin, V.G., Konkina, L.I.: New Methods in Dynamics of a Rigid Body. Ilim, Frunze (1989) in Russian

    Google Scholar 

  5. Bulgakov, B.V.: Applied Theory of Gyroscopes, 3rd edn. Moscow State Univ., Moscow (1976) in Russian

    Google Scholar 

  6. Beletsky, V.V.: Motion of an Artificial Satellite about its Center of Mass. Israel Program for Scientific Translation, Jerusalem (1966)

    Google Scholar 

  7. Beletsky, V.V.: Spacecraft Attitude Motion in Gravity Field. Moscow State Univ., Moscow (1975) in Russian

    Google Scholar 

  8. 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)

    Article  MathSciNet  Google Scholar 

  9. Moiseev, N.N.: Asymptotic Methods of Nonlinear Mechanics. Nauka, Moscow (1981) in Russian

    Google Scholar 

  10. Akulenko, L.D.: Asymptotic Methods of Optimal Control. Nauka, Moscow (1987) in Russian

    Google Scholar 

  11. Akulenko, L.D.: Problems and Methods of Optimal Control. Kluwer, Dordrecht (1994)

    Book  MATH  Google Scholar 

  12. Akulenko, L.D.: Higher-order averaging schemes in systems with fast and slow phases. J. Appl. Math. Mech. 66(2), 153–163 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  13. Arnold, V.I., Kozlov, V.V., Neishtadt, A.I.: Mathematical Aspects of Classical and Celestial Mechanics. Springer, Berlin (2007)

    MATH  Google Scholar 

  14. 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

    Google Scholar 

  15. Akulenko, L.D.: Higher-order averaging schemes in the theory of non-linear oscillations. Prikl. Mat. Mekh. 65(5), 843–853 (2001) in Russian

    Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. Chernousko, F.L.: Motion of a Rigid Body with Viscous-Fluid-Filled Cavities. Computing Center AN SSSR, Moscow (1968) in Russian

    Google Scholar 

  18. Chernousko, F.L.: The Movement of a Rigid Body with Cavities Containing a Viscous Fluid. NASA, Washington (1972)

    Google Scholar 

  19. 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)

    Article  Google Scholar 

  20. 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

    Google Scholar 

  21. Appel, P.: Traite de Mechanique Rationnelle. Gauthier – Villars, Paris (1953)

    Google Scholar 

  22. Landau, L.D., Lifshitz, E.M.: Course of Theoretical Physics, Mechanics, vol. 1. Pergamon Press, Oxford (1976)

    Google Scholar 

  23. Arnold, V.I.: Geometrical Methods in the Theory of Ordinary Differential Equations. Springer, London (2012)

    Google Scholar 

  24. 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)

    Google Scholar 

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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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53927-0

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