Abstract
To meet spacecraft attitude determination and control requirements, we must frequently predict the attitude motion for a given set of initial conditions. This requires specifying the differential equations governing the attitude motion and a method of solution. The general methods used for attitude prediction, given appropriate torque models, are discussed in Section 17.1. The necessary modeling of the environmental and internal torques is described in Sections 17.2 and 17.3. Torque modeling during orbit maneuvers is discussed in Section 17.4.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramson, H. N., W. H. Chu, and G. E. Ramsleben, Jr., “Representation of Fuel Sloshing in Cylindrical Tanks by an Equivalent Mechanical Model,” Am. Rocket Society J., Vol. 31, p. 1967–1705, 1961.
Abramson, H. N., editor, The Dynamic Behavior of Liquids in Moving Containers, NASA SP-106, 1966.
Bastow, J. G., editor, Proceedings of the Magnetic Workshop, March 30-April 1, 1965, JPL Tech Memo 32–316, 1965.
Bauer, H. F., Theory of the Fluid Oscillations in a Circular Cylindrical Ring Tank Partially Filled with Liquid, NASA TN D-557, 1960.
Bauer, H. F., Fluid Oscillations in the Containers of a Space Vehicle and Their Influence Upon Stability, NASA TR R-187, 1964.
Beard, R. M., J. E. Kronenfeld, and E. Areu, Small Astronomy Satellite-2 (SAS-2), Dynamic Attitude Determination System (DYNAD) Mathematical Models and Results from Processing, Comp. Sc. Corp., 3000–33900–01 TR, Dec. 1974.
Beletskii, V. V., Motion of an Artifical Satellite About its Center of Mass, NASA TT F-429, 1966.
Bourke, Roger D., Stephen R. McReynolds, and Kathryn L. Thuleen, “Translational Forces on Mariner V from the Attitude Control System,” J. Spacecraft, Vol. 6, p. 1063–1066, 1969.
Butcher, J. C., “On the Attainable Order of Runge-Kutta Methods,” Math. Comp. Vol. 19, p. 408–417, 1965.
Carnahan, Brice, H. A. Luther, and James O. Wilkes, Applied Numerical Methods, New York: John Wiley & Sons, Inc., 1969.
Chen, L. C. and J. J. McEnnan, SIRIO Attitude Analysis Postlaunch Report, Comp. Sc. Corp., CSC/TM-77/6264, Oct. 1977.
Childs, Dara W., “A Movable-Mass Attitude-Stabilization System for Artificial-g Space Station,” J. Spacecraft, Vol. 8, p. 829–834, 1971.
Childs, Dara W., and Therman L. Hardison, “A Movable-Mass Attitude-Stabilization System for Cable-Connected Artificial-g Space Station,” J. Spacecraft, Vol. 11, p. 165–172, 1974.
Chubb, W. B, H. F. Kennel, C. C. Rupp, and S. M. Seltzer, “Flight Performance of Skylab Attitude and Pointing Control System,” J. Spacecraft, Vol. 12, p. 220–227, 1975.
Cloutier, Gerald J., “Elevation Stepping of Gimballed Devices on Rotor-stablized Spacecraft,” J. Spacecraft, Vol. 12, p. 511–512. 1975.
Davidson, John R. and Robert L. Armstrong, “Effect of Crew Motion on Spacecraft Orientation,” AIAA J., Vol. 9, p. 232–238, 1971.
Dobrotin, B., E. A. Laumann, and D. Prelewicz, Mariner Limit Cycles and Self-Disturbance Torques, AIAA Paper No. 69–844, AIAA Guidance, Control, and Flight Mechanics Conference, Aug. 1969.
Dodge, Franklin T. and Daniel D. Kana, “Moment of Inertia and Damping of Liquids in Baffled Cylindrical Tanks,” J. Spacecraft, Vol. 3, p. 153–155, 1966.
Dodge, F. T., and L. R. Garza, “Experimental and Theoretical Studies of Liquid Sloshing at Simulated Low Gravities,” J. Appl. Mech., Vol. 34, p. 555–562, 1967.
Droll, P. W. and E. J. Iuler, “Magnetic Properties of Selected Spacecraft Materials,” Proc., Symposium on Space Magi.nic Exploration and Technology, Engineering Report No. 9, p. 189–197, 1967.
Edward, Terry L. and Marshall H. Kaplan, “Automatic Spacecraft Detumbling by Internal Mass Motion,” AIAA J., Vol. 12, p. 496–502, 1974.
Edwards, D. K. and J. T. Bevans, “Radiation Stresses on Real Surfaces,” AIAA Journal, Vol. 3, p. 522–523, 1965.
Enright, W. H., and T. E. Hull, “Test Results on Initial Value Methods for Non-Stiff Ordinary Differential Equations,” SIAM J. Numer. Anal., Vol. 13, p. 944–961, 1976.
Fang, Bertrand T., “Kinetic Energy and Angular Momentum About the Variable Center of Mass of a Satellite,” AIAA J., Vol. 3, p. 1540–1542, 1965.
Fish, V. R. and B. G. Chmielewski, Flight Program Requirements Document for the High Energy Astronomy Observatory-B Attitude Control and Determination Subsystem (FPH-R), TRW Systems Group Doc. No. DO1137B, April 1977.
Gebman, Jean R. and D. Lewis Mingori, “Perturbation Solution for the Flat Spin Recovery of a Dual-Spin Spacecraft,” AIAA J., Vol. 14, p. 859–867, 1976.
General Electric Co., Plume and Thrust Tests on Nimbus Attitude Control Nozzles, Information Release 9461–135, May 22, 1964.
Gottlieb, D. M., C. M. Gray, and S. G. Hotovy, An Approximate Shadowing Technique to Augment the Aerodynamic Torque Model in the AE-C Multi-Satellite Attitude Prediction and Control Program (MSA P/AE), Comp. Sc. Corp., 3000–257-01TM, Oct. 1974.
Grubin, C., “Dynamics of a Vehicle Containing Moving Parts,” J. of Applied Mech., Vol. 29, p. 486–488, 1962.
Hamming, R. W., Numerical Methods for Scientists and Engineers. New York: McGraw-Hill, Inc., 1962.
Henrici, P. H., Discrete Variable Methods in Ordinary Differential Equations. New York: John Wiley & Sons, Inc., 1962.
Henrici, P. H., Elements of Numerical Analysis. New York: John Wiley & Sons, Inc., 1964.
Hildebrand, F. B., Introduction to Numerical Analysis, New York: McGraw-Hill, Inc., 1956.
Holland, R. L. and H. J. Sperling, “A First-order Theory for the Rotational Motion of a Triaxial Rigid Body Orbiting an Oblate Primary,” Astronomical Journal, Vol. 74, p. 490, 1969.
Hooper, L., Private Communication, 1977.
Hull, T. E., W. H. Enright, B. M. Fellen, and A. E. Sedgwick, “Comparing Numerical Methods for Ordinary Differential Equations,” SIAM J. Numer. Anal., Vol. 9, p. 603–637, 1972.
Hultquist, P. F., “Gravitational Torque Impulse on a Stabilized Satellite,” ARS Journal, Vol. 31, p. 1506–1509, 1961.
Iwens, R. P. and R. Farrenkopf, Performance Evaluation of a Precision Attitude Determination System (PADS), AIAA Paper No. 71–964, Guidance Control and Flight Mechanics Conference, Hofstra U., Hempstead, NY, Aug. 1971.
Katz, Paul, “Comments on ‘A Re-Evaluation of Jet Damping’,” J. Spacecraft, Vol. 5, p. 1246, Oct. 1968.
Keat, J. and M. Shear, Apogee Motor Firing Dynamics Study for the Communications Technology Satellite, Comp. Sc. Corp, 3000–05600–08TN, May 1974.
Koelle, H. H., editor, Handbook of Astronautical Engineering. New York: McGraw-Hill Book Co., Inc., 1961.
Lambert. J. D., Computational Methods in Ordinary Differential Equations. New York: John Wiley & Sons, Inc., 1973.
Langley Research Center, Propellant Slosh Loads, NASA SP-8009, Aug. 1968.
Lawrence, H. R., C. J. Wang, and R. B. Reddy, “Variational Solution of Fuel Sloshing Modes,” Jet Propulsion, Vol. 128, p. 729–736, 1958.
Lomen, D. O., Liquid Propellant Sloshing in Mobile Tanks of Arbitrary Shape, NASA CR-222, April 1965a.
Lomen, D. O., Digital Analysis of Liquid Propellant Sloshing in Mobile Tanks with Rotational Symmetry, NASA CR-230, May 1965b.
Mariner-Mars 1964 Project Report: Mission and Spacecraft Development, vol. I: From Project Inception through Midcourse Maneuver, JPL, Tech. Report 32740, March 1965.
Marshall Space Flight Center, The Meteroid Satellite Project Pegasus, First Summary Report, NASA TN D-3505, 1966.
Massey, W. A., Pioneer VI Orientation Control System Design Survey, Control System Laboratory, TRW, Report No. 06314–6006-R001, Rev. 1 (Contract NAS 12–110), Sept. 1968.
McElvain, R. J. and L. Schwartz, “Minimization of Solar Radiation Pressure Effects for Gravity-Gradient Stabilized Satellites,” J. Basic Eng., p. 444–451, June 1966.
Mobley, F. F. and R. E. Fischell, Orbital Results from Gravity-G radient Stabilized Satellite, APL, Johns Hopkins U. Tech. Memo. TG-826, Oct. 1966. (Also available from NASA Ames Research Center as Symposium on Passive Gravity Gradient Stabliazation, p. 237, 1965.)
Moiseev, N. N. and A. A. Petrov, “The Calculation of Free Oscillations of a Liquid in a Motionless Container,” Advances in Applied Mech. New York: Academic Press, Inc., Vol. 9, p. 91–154, 1966.
NASA, Application Technology Satellite, Vol. 1–8, Tech. Data Report. GSFC, NASA TM X-61130, 1968.
NASA, Spacecraft Magnetic Torques, NASA SP-8018, March 1969a.
NASA, Spacecraft Radiation Torques, NASA SP-8027, Oct. 1969b.
NASA, Research Center Pioneer Project Office, Pioneer VI Mission, NASA Ames Research Center, Moffet Field, CA, May 22, 1967.
Nidey, R. A., “Gravitational Torque on a Satellite of Arbitrary Shape,” ARS Journal, Vol. 30, p. 203–204, 1960.
Nidey, R. A., “Secular Gravitational Torque on a Satellite in a Circular Orbit,” ARS Journal, Vol. 31, p. 1032, 1961.
Page, G., Private Communication, Nov. 1975.
Papis, T., “Comments on ‘A Re-Evaluation of Jet Damping’,” J. Spacecraft, Vo. 5, p. 1246–1247, Oct. 1968.
Poli, Corrado R., “Effect of Man’s Motion on the Attitude of a Satellity,” J. Spacecraft, Vol. 4, p. 15–20, 1971.
Ralston, A., A First Course in Numerical Analysis. New York: McGraw-Hill, Inc., 1965.
Rathayya, J. V., Sloshing of Liquid in Axisymmetric Ellipsoidal Tanks, AIAA Paper No. 65–114, Jan. 1965.
Roberson, R. E., “Torques on a Satellite Vehicle From Internal Moving Parts,” J. of Applied Mech., Vol. 25, Trans. ASME, Vol. 80, p. 196–200, 1958a.
Roberson, R. E., “Gravitational Torque on a Satellite Vehicle,” J. Franklin Institute, Vol. 265, p. 13–22, 1958b.
Roberson, R. E., “Alternate Form of a Result by Nidey,” ARS Journal, Vol. 31, p. 1292, 1961.
Schaaf, S. A. and P. L. Chambré, Flow of Rarefied Gas. Princeton, N.J.: Princeton University Press, 1961.
Schalkowski, S. and M. Harris, Spacecraft Mass Expulsion Torques, NASA SP-8034, Dec. 1969.
Suttles, T. E. and R. E. Beverly, Model for Solar Torque Effects on DSC S II, AAS/AIAA paper No. AAS 25–095, AAS/AIAA Astrodynamics Specialist Conference, Nassau, Bahamas, July 1975.
Tandon, G. K. and P. M. Smith, Communications Technology Satellite (CTS) Postlaunch Report, Comp. Sc. Corp., CSC/TM-76/6104, May 1976.
Thomson, W. T. and Y. C. Fung, “Instability of Spinning Space Stations Due to Crew Motion,” AIAA J., Vol. 3, p. 1082–1087, 1965.
Thomson, W. T. and G. S. Reiter, “Jet Damping of a Solid Rocket: Theory and Flight Results,” AIAA J., Vol. 3, p. 413–417, 1965.
Tidwell, N. W., “Modeling of Environmental Torques of a Spin-Stabilized “Spacecraft in a Near-Earth Orbit,” J. Spacecraft, Vol. 7, p. 1425–1435, 1970.
Victor, P. T., Initial Stabilization Control Nozzle Plume Impingement Study, General Electric Co., Data Memo 1:57, Oct. 1964.
Visti, J. P., Theory of the Spin of a Conducting Satellite in the Magnetic Field of the Earth. Ballistic Research Laboratories, Aberdeen, MD, Report No. 1020, July 1957.
Warner, G. C. and V. W. Snyder, “A Re-Evaluation of Jet Damping,” J. Spacecraft, Vol. 5, p. 364–366, March 1968.
White, R. A., H. W. Robinson, and D. I. Berman, STORM SAT Ground System Concept Study, Comp. Sc. Corp. CSC/SD-76/6088, Nov. 1976.
Wilcox, J. C., “A New Algorithm for Strapped-Down Inertial Navigation,” IEEE Trans. on Aerospace and Electronic Systems, Vol. AES-3, no. 5, p. 796–802, Sept, 1967.
Yong, K., NASA Goddard Space Flight Center Sounding Rocket Division, MASS Program Documentation, AVCO Systems Division: Seabrook, MD, Aug. 1974.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1978 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Wertz, J.R. (1978). Attitude Prediction. In: Wertz, J.R. (eds) Spacecraft Attitude Determination and Control. Astrophysics and Space Science Library, vol 73. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9907-7_17
Download citation
DOI: https://doi.org/10.1007/978-94-009-9907-7_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-277-1204-2
Online ISBN: 978-94-009-9907-7
eBook Packages: Springer Book Archive