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Numerical Procedures for the Attitude and Orbital Maneuvers Computation of a Spin-Stabilised Satellite

  • Conference paper
Space Engineering

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 15))

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Abstract

One purpose of this paper is to recall the mathematical procedures which can be used for integrating ordinary nonlinear differential equations. Actually, in digital computations matters such as machine memory and running time, have to be weighted against accuracy and stability and different procedures should be employed even for a given system following the class (i.e. the accuracy and running time) of the expected results. Accordingly, the main aspects embedded in integrating methods based on local polynomial approximation are discussed to some extent, and first order stability conditions for the numerical procedures are worked out simply by applying the well known z-transform.

The second purpose of the paper is to present the basic analytical support for the maneuvers of attitude and the orbital corrections for a spin stabilized satellite. To that end the reference dynamic equations are first established and the basic applied control is discussed. This brings an example computation of great importance since solution accuracy and computer running time must both be optimized. An adapted Hamming procedure with variable steps seems the best mate to the problem, being about twice less time-consuming than an equal-accuracy iterative Runge-Kutta algorithm.

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Abbreviations

x, y, z, :

body-fixed axes

X, Y, Z, :

inertially-referred axes

F x , F y , F z :

components of the thrust along the body axes

J x , J y , J z :

principal moments of inertia of the satellite referred to the center of mass

j x , j y , j z :

rate of change of principal moments of inertia

l :

distance of the efflux surface from the center of mass

M :

mass of the satellite

ṁ :

is the mass flow distribution along the radius r of surface s of the divergent

Ṁ :

mass variation of the satellite

M x , M y , M z :

moments around the body-fixed axes (principal of inertia)

r :

actual radius of the divergent

ω x , ω y , ω z :

components about the body axes of the angular velocity

φ, ϑ, ψ :

yaw, roll and pitch angles

Ω x , Ω y , Ω z :

angular velocities of the ejected particles referred to the body axes in terms of radius r

ε x , ε y , ε z :

expulsion effects around the satellite axes.

References

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Author information

Authors and Affiliations

  1. Istituto di Meccanica Applicata alle Macchine, Università di Genova, Italy

    R. C. Michelini & G. Acaccia

  2. Div. Servosistemi ed Elettronica, Nuova San Giorgio S.p.A., Italy

    E. Gimelli & D. Dini

Authors
  1. R. C. Michelini
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  2. G. Acaccia
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  3. E. Gimelli
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  4. D. Dini
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Editor information

Editors and Affiliations

  1. Centro Studi Trasporti Missilistici, Rome, Italy

    G. A. Partel

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© 1970 D. Reidel Publishing Company, Dordrecht, Holland

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Michelini, R.C., Acaccia, G., Gimelli, E., Dini, D. (1970). Numerical Procedures for the Attitude and Orbital Maneuvers Computation of a Spin-Stabilised Satellite. In: Partel, G.A. (eds) Space Engineering. Astrophysics and Space Science Library, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-7551-7_7

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  • DOI: https://doi.org/10.1007/978-94-011-7551-7_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-011-7553-1

  • Online ISBN: 978-94-011-7551-7

  • eBook Packages: Springer Book Archive

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