Active deceleration of rotational motions of a dynamically asymmetric quasirigid body

Authors: Zinkevych Ya.S.

Year: 2016

Issue: 20

Pages: 128-134

Abstract

In this article a minimum-time problem of deceleration of rotations of a free rigid body is studied analytically and numerically. It is assumed that a body contains a spherical cavity filled with highly viscous fluid. The body is subjected to a retarding torque of viscous friction. It is assumed that such body is dynamically asymmetric. An optimal control law for deceleration of rotations of the body is synthesized, and the corresponding time and phase trajectories are determined.
The asymptotic approach made it possible to determine the control evolutions of the magnitude squared of the elliptic functions modulus k2, dimensionless kinetic energy and kinetic moment. The qualitative properties of the optimal motion were also found.
The obtained results allow us to build a synthesis of the optimal deceleration of rotations of satellites and spacecrafts. They can be used to analyze dynamics of controlled spacecrafts.

Tags: asymmetric body; cavity; optimal deceleration; resistive medium

Bibliography

  1. Chernous’ko F.L. Motion of a Rigid Body with Cavities Filled with Viscous Fluid at Small Reynolds Numbers.
    USSR Comput. Math. Math. Phys., 1965, no. 5, pp. 99-127.
  2. Akulenko L.D., Leshchenko D.D., Rachinskaya A.L. Evolution of Rotations of a Satellite with a Cavity Filled with Viscous Fluid in Mechanics of Solids. OOO “Nord Komp’yuter”. Donetsk, 2007, issue 37, pp. 126-139.
  3. Akulenko L.D., Leshchenko D.D., and Chernous’ko F.L. Fast Rotation of a Heavy Solid Body in a Dragging Medium about a Fixed Point. Izv. Akad. Nauk SSSR, Mekhanika Tverdogo Tela, 1982, no. 3, pp. 5-13.
  4. Koshlyakov V.N. Problems in Dynamics of Solid Bodies and in Applied Gyroscope Theory: Analitical Metods. Moscow: Nauka, 1985. 288 p.
  5. Routh E.J. Dynamics of a System of Rigid Bodies. Mineola, N.Y.: Dover, 2005; Moscow: Nauka, 1983, vol. 2, 544 p.
  6. Akulenko L.D., Leshchenko D.D., Rachinskaya A.L. Evolution of the Satellite Fast Rotation due to the Gravitational Torque in a Dragging Medium. Mech. Solids, 2008, no 43, pp. 173-184.
  7. Akulenko L.D. Problems and Methods of Optimal Control. Kluwer, Dordrecht-Boston-London, 1994. 360 p.
  8. Akulenko L.D., Leshchenko D.D. Optimal Deceleration of Rotation of a Solid Body with Internal Degrees of Freedom. Izv. RAN. TiSU, 1995, no. 2, pp. 115-122.
  9. Leshchenko D.D. Optimal Damping of Rotations of a Solid Body with Interior Degrees of Freedom with Respect to Speed. J. Comput. Syst. Sci. Int., 1996, no 5, pp. 74-79.
  10. Akulenko L.D., Leshchenko D.D., Rachinskaya A.L. Optimal Deceleration of Rotation of a Dynamically Symmetric Body with a Cavity Filled with Viscous Liquid in a Resistive Medium. J. Comput. Syst. Sci. Int., 2010, no. 49, pp. 222-226.
  11. Akulenko L.D., Zinkevich Ya.S., Leshchenko D.D. Optimal Rotation Deceleration of a Dynamically Asymmetric Body in a Resistant Medium. J. Comput. Syst. Sci. Int., 2011, no. 50, pp. 14-19.
  12. Beletskii V.V. Motion of a Satellite about its Center of Mass. Moscow: Nauka, 1965. 416 p.
  13. Gradshtein I.S., Ryzhik I.M. Tables of Integrals, Series, and Products. Moscow: Nauka, 1971; Academic, New York, 1965; San Diego:Academic, 1980. 1108 p.
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