Abstract
Optimal response criteria are developed for the passive attitude control of a composite spacecraft. The physical structure is uniquely different from multi-body systems in that the components are independently and passively stabilized, here the primary body is gravity oriented while the auxiliary body, through geometry selection, is aerodynamically controlled. The Routh-Hurwitz stability criterion is used to obtain the parameter bounds for stability about the preferred dynamic equilibrium position. Further, the least damped mode concept with respect to the roots of the characteristic equation is used to predict conditions for optimum performance. Numerically generated optimal response curves for a satellite in circular orbit show very rapid damping rates for large disturbances up to ten degrees. Under these conditions, and in the absence of external disturbances, course alignment was reached within several orbits and fine pointing accuracy attainable up to altitudes of 650 kilometers.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- A y ,B y ,C y :
-
mass moments of inertia about they 1,y 2,y 3 axes respectively
- A z ,B z ,C z :
-
mass moments of inertia about thez 1,z 2,z 3 axes respectively
- C d :
-
aerodynamic drag coefficient
- F :
-
first moment of area about thez 2-axis
- [I] y , [I] z :
-
inertia matrices of the main and auxiliary bodies respectively
- K :
-
hinge spring constant
- K y :
-
main body inertia ratio,(A y −C y )/B y
- K z :
-
auxiliary body inertia ratio,(A z −C z )/B z
- M A :
-
aerodynamic torque
- O :
-
center of force
- P a :
-
aerodynamic parameter
- P c :
-
damping parameter
- P K :
-
spring parameter
- Q i :
-
generalized force associated with theith generalized co-ordinate,q i
- R :
-
distance from the center of force to the system center of mass
- [T] ij :
-
transformation matrix between theith andjth co-ordinate sets
- T ij :
-
appropriate element of[T] ij
- T y :
-
kinetic energy of the main body
- T z :
-
kinetic energy of the auxiliary body
- V, (V c ):
-
satellite orbital velocities (V c =reference velocity=circular orbit velocity atr e )
- V Gy :
-
gravitational potential of main body
- V Gz :
-
gravitational potential of auxiliary body
- V r :
-
relative velocity of the satellite with respect to the atmosphere
- X(x 1,x 2,x 3):
-
orbital attitude-reference co-ordinate set
- Y(y 1,y 2,y 3):
-
body-fixed principal co-ordinates for the main body located at the system center of mass
- Z(z 1,z 2,z 3):
-
body-fixed principal co-ordinates for the auxiliary body located at the system center of mass
- a i :
-
coefficients defined in Equations (30) and (31)
- c :
-
hinge damper constant
- d :
-
distance from the system center of mass to the auxiliary body center of mass
- e :
-
orbit eccentricity
- h, (h 0):
-
satellite altitude, (h 0-reference altitude defined in Equation (14))
- m y :
-
mass of main body
- m z :
-
mass of auxiliary body
- m :
-
(m y +m z )
- r :
-
location vector of an element of mass measured from 0
- r e :
-
Earth radius
- [t] i :
-
transformation matrix for theith rotation only
- s :
-
Laplace variable
- θ:
-
angular displacement ofR measured from perigee
- ψ, α:
-
Euler angles locating the system in pitch relative toX
- λ j :
-
roots of the characteristic equation
- β:
-
system inertia ratio,K z /K y
- δ:
-
system inertia ratio,B z /B y
- μ:
-
gravitational field constant
- ϱ:
-
location vector of an elemental mass measured from the system mass center
- ϱ h , (ϱ0):
-
atmospheric density at altitudeh, (h 0)
- τ:
-
damping index
- ω:
-
absolute angular velocity in terms of body-fixed co-ordinates
References
Brereton, R. C.: 1967, ‘A Stability Study of Gravity Oriented Satellites’, Ph.D. dissertation, University of British Columbia, Vancouver, Canada.
Connell, G. H.: 1969, ‘Optimal Configurations for Hinged, Two-Body Satellites’,J. of Spacecraft and Rockets 6, 1024–1030.
Cook, G. E.: 1960, ARC Current Paper No. CP523, Ministry of Aviation, H.M.S.O., London.
Flanagan, R. C. and Modi, V. J. 1971a, ‘Effect of Environmental Forces on the Attitude of Gravity Oriented Satellites—Part 1: High Altitude Orbits’,Aeronaut. J. 75, 783–793.
Flanagan, R. C. and Modi, V. J.: 1971b, ‘Librational Damping of a Gravity Oriented System using Solar Radiation Pressure’,Aeronaut. J. 75, 560–564.
Flanagan, R. C. and Modi, V. J.: 1972, ‘Effect of Environmental Forces on the Attitude of Gravity Oriented Satellites—Part 3: Low Altitude Orbits Accounting for Aerodynamic Forces’,Aeronaut. J. 76, 34–40.
Flanagan, R. C. and Rangarajan, R.: 1973, ‘Liapunov Stability Analysis and Attitude Response of a Passively Stabilized Space System’,Astronaut. Acta 18, 21–34.
Fletcher, H. J., Rongved, L., and Yu, E. Y.: 1963, ‘Dynamic Analysis of a Two-Body Gravitationally Oriented Satellite’,Bell System Technical J. 2239–2266.
Jensen, J., Townsend, G., Kork, J., and Kraft, D.: 1962,Design Guide to Orbital Flight, McGraw-Hill, New York, pp. 179–264.
Klemperer, W. B. and Baker, R. M., Jr.: 1957, ‘Satellite Libration’,Astronaut. Acta 3, 16–27
Ravindran, R.: 1971, ‘Optimal Aerodynamic Attitude Stabilization of Near Earth Satellites’, UTIAS Report No. 164, University of Toronto, Toronto, Canada.
Yu, E. Y.: 1964, ‘Long-Term Coupling Effects Between the Librational and Orbital Motions of a Satellite,’,AIAA J. 2, 553–555.
Zajac, E. E.: 1962, ‘Damping of a Gravitationally Oriented Two-Body Satellite,ARSJ. 1871–1875.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rangarajan, R., Flanagan, R.C. Parameter optimization and optimal attitude response of a passive environmentally controlled space system. Celestial Mechanics 12, 231–249 (1975). https://doi.org/10.1007/BF01230215
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01230215