The librational motion of a satellite depends on the gravity gradient, aerodynamic, and magnetic torques, on the moments of inertia of the satellite and on some less significant influences as solar radiation, the electrical field of the earth, the meteorite impacts. Only the gravity gradient torque can be considered with a great degree of accuracy as deterministic. Aerodynamic and magnetic torques can be treated as deterministic quantities only in a very rough first approximation. In reality these torques always have stochastic components caused by the fluctuations of the atmospheric density and the earth’s magnetic field. Furthermore, the calculation of these torques for a given satellite is based on assumptions whose nature is indeed stochastic. The same is true for influences caused by solar radiation, meteorite impacts, and electrical field of the earth. The moments of inertia of a satellite are deterministic only for completely rigid bodies. The uncontrolled thermo-elastic oscillations of the stabilizing rods, antennae, and sun cell panels, the motion of the crew, the wobbling of liquid in the tanks etc. make the concept of an ideally rigid satellite questionable. Thus, the moments of inertia have to be regarded as stochastic quantities too. In consequence of the stochastical nature of the mentioned outer and inner influences the librational motion of a satellite is a stochastic process and has to be described by stochastic differential equations. The first conception of these equations was given in the late forties by Itô [1]. In the following twenty years this first conception was developed by the works of Skorokhod, Bucy, Kushner, Khasminski a.o. The first books on this subject appeared in the last few years: Bucy [2], Kushner [3], Gikhmanand Skorokhod [4], Khasminski [5]. Today the Theory of Stochastic Differential Equations and the Theory of Stochastic Stability are powerful tools in the applications and especially in the dynamics of satellites.


Solar Radiation Stochastic Differential Equation Gravity Gradient Stochastic Stability Stochastic Component 
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Copyright information

© Springer-Verlag Wien 1970

Authors and Affiliations

  • Peter Sagirow
    • 1
  1. 1.Stuttgart UniversityGermany

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