Abstract
An implementation of the momentum transfer method for spacecraft attitude acquisition of momentum wheel stabilized geostationary satellites is presented, in which the wheel speed is varied in a predeterminable manner to reduce the nutation usually associated with the method. The implementation is found to be capable of achieving the transfer to the desired zero nutation end point with 5° to 20° of residual nutation in practical situations without additional nutation damping. The transfer time is typically 10–30 min. The implementation is described in terms of the momentum sphere and energy ellipsoid. The detailed functional dynamics and parametric relationships are given in terms of phase planes and elliptic integral solutions. Feasibility of the implementation is shown to be dependent on the moment of inertia configuration and the degree to which tolerances on moments of inertia, satellite spin rate, and wheel speed are predeterminable.
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Abbreviations
- A, B, C :
-
Principal moments of inertia of the total spacecraft
- b 1,b 2,b 3 :
-
Unit vectors parallel to principal axes
- E, E(t) :
-
Energy of the spacecraft body (excludes the spin energy of momentum wheel)
- E 0 :
-
Initial energy of the spacecraft (wheel not spinning)
- E c :
-
A constant arbitrary value ofE(t)
- E i :
-
Energy after an impulse which causes ɛ to equal zero, Equation (13)
- E 2 :
-
The constant value ofE during Stage 2
- E 3 :
-
Energy at the end of Stage 3
- E s :
-
The separatrix value ofE, i.e.E when ɛ=0
- H 0,H 0 :
-
Angular momentum vector of the total spacecraft
- H x ,H y ,H z :
-
Variable components ofH 0 resolved with respect tob 1,b 2, andb 3
- J :
-
Moment of inertia of the momentum wheel
- L :
-
The slope of the wheel speed profile, Equation (31)
- L y :
-
Momentum wheel torque
- m :
-
Direction cosine of the angle, θ, betweenH 0 andb 2
- m 1,m 2 :
-
Constant values ofm
- O :
-
The centre of the momentum sphere
- Oxyz :
-
Spacecraft coordinate axes
- P :
-
Represents a state on the momentum sphere and energy ellipsoid
- s :
-
Momentum wheel speed
- s 2 :
-
Constant value ofs during Stage 2
- s i :
-
Wheel speed after an impulse which causes ɛ to be zero
- t :
-
Time
- Δt 1, Δt 2, Δt 3 :
-
Elapsed time for Stages 1, 2, and 3 respectively
- α 1 toα 4 :
-
Roots of Equation (19) (poles on the phase plane)
- ɛ:
-
Parameter defined in Equation (9)
- θ:
-
cos−1 m
- θ2 :
-
The value of θ at the termination of Stage 2
- θ min :
-
The minimum of the periodic function θ(t) (during Stage 2)
- ω x , ω y , ω z :
-
Angular rates of spacecraft body
- ω0 :
-
Initial value of ω z
- K m :
-
Curvature of the momentum sphere
- K xy ,K yz :
-
Curvatures of the principal lines of the energy ellipsoid at (O,H 0,O), in theOH x H y ) and (OH y H z ) planes respectively
References
Barba, P. M. and Aubrun, J. N.: 1976,AIAA Journ. 14, 1382.
Erdelyi, A.: 1953,Higher Transcendental Functions, Vol, II, McGraw-Hill, pp. 307–309.
Gebman, J. R. and Mingori, D. L.: 1976,AIAA Journ. 14, 859.
Kaplan, M. H. and Patterson, T. C.: 1976,Comsat Technical Review 6, 1.
Staley, D. A.: 1978,An Analytical Investigation of Momentum Exchange Attitude Acquisition Without a Nutation Damper, ANCON-R. 785, ANCON Space Technology Corporation, Thornhill, Ontario, Canada.
Staley, D. A.: 1979,Simulation of a Momentum Exchange Attitude Acquisition Technique, ANCON-R. 787, ANCON Space Technology Corporation, Thornhill, Ontario, Canada.
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Vigneron, F.R., Staley, D.A. Satellite attitude acquisition by momentum transfer-the controlled wheel speed method. Celestial Mechanics 27, 111–130 (1982). https://doi.org/10.1007/BF01271687
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DOI: https://doi.org/10.1007/BF01271687