Satellites with Moving Parts

  • Peter Sagirow
Part of the International Centre for Mechanical Sciences book series (CISM, volume 57)


In this section two completely independent examples of satellites with moving parts are considered. In both cases the noise is caused by the non-rigidity of the satellite. However, the resulting stochastic models are quite different. In the first case the mass distribution of the satellite remains constant in spite of the moving parts. The problem leads to a common linear stochastic differential equation. In the second case the mass distribution of the satellite varies in dependence of the inner motion. The stochastic modeling results in an unusual nonlinear stochastic differential equation.


Stochastic Model Stochastic Differential Equation Pitch Motion Shaping Filter Driving Torque 
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  1. [1]
    Itô, K.: On Stochastic Differential Equations, Memoirs of Amer. Math. Soc., 1951.Google Scholar
  2. [2]
    Bucy, R.S., Joseph, P.D.: Filtering for Stochastic Processes with Applications to Guidance, J. Wiley & Sons, 1968.Google Scholar
  3. [3]
    Kushner, H.J.: Stochastic Stability and Control, Academic Press, 1967.Google Scholar
  4. [4]
    Gikhman, J.J., Skorokhod, A.V.: Stochastic Differential Equations (Russ.) Kiev, 1968.Google Scholar
  5. [5]
    Khas’minski, R.S.: The stability of Systems of Differential Equations With Random Disturbances of Parameters (Russ.),Moscow, 1969.Google Scholar
  6. [6]
    McKean, H.P.: Stochastic Integrals, Academic Press, 1969.Google Scholar
  7. [7]
    Stratonovich, R.L.: A New Representation for Stochastic Integrals and Equations, Siam J. Control 4, 1966.Google Scholar
  8. [8]
    Loève, M.: Probability Theory, Van Nostrand Co., 1963.Google Scholar
  9. [9]
    Doob, J.: Stochastic Processes, J. Wiley & Sons, 1960.Google Scholar
  10. [10]
    Dynkin, E.B.: Die Grundlagen der Theorie der Markoffschen Prozesse, Springer, 1961.Google Scholar
  11. [11]
    Aleksejev, K.B., Bebenin G.G.: Space Vehicle Control, NASA TTS-9336, Ohio, 1966.Google Scholar
  12. [12]
    Beletzkij, V.V.: Motion of an Artificial Satellite About its Centre of Mass, Jerusalem, 1966.Google Scholar
  13. [13]
    Sagirow,P.S., Satellitendynamik, BI-Verlag, 1970.Google Scholar
  14. [14]
    Schrello, D.M.: Dynamic Stability of Aerodynamically Responsive Satellites, Journ. Aerosp. Sci., 1962.Google Scholar
  15. [15]
    Sheporaitis, L.P.: Stochastic Stability of a Satellite Influenced by Aerodynamic and Gravity Gradient Torques,AIAA 8th Aerosp. Sci. Meeting, New-York, Jan. 1970.Google Scholar
  16. [16]
    Hahn, W.: Stability of Motion, Springer, 1967.Google Scholar
  17. [17]
    Kalman, R.E., Falb, P.L., Arbib, M.A.: Topics in Mathematical System Theory, McGraw-Hill, 1969.Google Scholar
  18. [18]
    Loh, W.H.T.: Dynamics and Thermodynamics of Planetary Re-entry, Prentice-Hall, Engle wood Cliffs., 1963.Google Scholar
  19. [19]
    Citron, S.I., and Meir, T.C.: An Analytic Solution for Entry into Planetary Atmospheres, AIAA Journ., Vol. 3, No. 3, 1965.Google Scholar
  20. [20]
    Handbook of Geophysics and Space Environments, McGraw-Hill, 1966.Google Scholar
  21. [21]
    King-Hele, D.: Theory of Satellite Orbits in an Atmosphere, Butterworths, 1964.Google Scholar
  22. [22]
    Weiss, G.R.: Re-Entry Dispersions Due to Atmospheric Uncertainties, Journ. of Spacecraft and Rockets, Vol. 6, Nr. 10, 1969.Google Scholar
  23. [23]
    Krementulo, V.V.: On Optimal Stabilization of a Rigid Body with Fixed Point by Means of Flywheels, PMM 30, 1966.Google Scholar
  24. [24]
    Pestel, E.D., Leckie, F.A.: Matrix Methods in Elastomechanics, McGraw-Hill, 1963.Google Scholar
  25. [25]
    Itô, K. and McKean, H.P.: Diffusion Processes and Their Sample Paths, Springer, 1965.Google Scholar

Copyright information

© Springer-Verlag Wien 1970

Authors and Affiliations

  • Peter Sagirow
    • 1
  1. 1.Stuttgart UniversityGermany

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