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Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 73))

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.

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References

  1. 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.

    Google Scholar 

  2. Abramson, H. N., editor, The Dynamic Behavior of Liquids in Moving Containers, NASA SP-106, 1966.

    Google Scholar 

  3. Bastow, J. G., editor, Proceedings of the Magnetic Workshop, March 30-April 1, 1965, JPL Tech Memo 32–316, 1965.

    Google Scholar 

  4. Bauer, H. F., Theory of the Fluid Oscillations in a Circular Cylindrical Ring Tank Partially Filled with Liquid, NASA TN D-557, 1960.

    Google Scholar 

  5. Bauer, H. F., Fluid Oscillations in the Containers of a Space Vehicle and Their Influence Upon Stability, NASA TR R-187, 1964.

    Google Scholar 

  6. 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.

    Google Scholar 

  7. Beletskii, V. V., Motion of an Artifical Satellite About its Center of Mass, NASA TT F-429, 1966.

    Google Scholar 

  8. 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.

    Article  Google Scholar 

  9. Butcher, J. C., “On the Attainable Order of Runge-Kutta Methods,” Math. Comp. Vol. 19, p. 408–417, 1965.

    Article  MathSciNet  MATH  Google Scholar 

  10. Carnahan, Brice, H. A. Luther, and James O. Wilkes, Applied Numerical Methods, New York: John Wiley & Sons, Inc., 1969.

    MATH  Google Scholar 

  11. Chen, L. C. and J. J. McEnnan, SIRIO Attitude Analysis Postlaunch Report, Comp. Sc. Corp., CSC/TM-77/6264, Oct. 1977.

    Google Scholar 

  12. Childs, Dara W., “A Movable-Mass Attitude-Stabilization System for Artificial-g Space Station,” J. Spacecraft, Vol. 8, p. 829–834, 1971.

    Article  Google Scholar 

  13. 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.

    Article  Google Scholar 

  14. 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.

    Article  Google Scholar 

  15. Cloutier, Gerald J., “Elevation Stepping of Gimballed Devices on Rotor-stablized Spacecraft,” J. Spacecraft, Vol. 12, p. 511–512. 1975.

    Article  Google Scholar 

  16. Davidson, John R. and Robert L. Armstrong, “Effect of Crew Motion on Spacecraft Orientation,” AIAA J., Vol. 9, p. 232–238, 1971.

    Article  MATH  Google Scholar 

  17. 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.

    Google Scholar 

  18. 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.

    Article  Google Scholar 

  19. 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.

    Article  Google Scholar 

  20. 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.

    Google Scholar 

  21. Edward, Terry L. and Marshall H. Kaplan, “Automatic Spacecraft Detumbling by Internal Mass Motion,” AIAA J., Vol. 12, p. 496–502, 1974.

    Article  Google Scholar 

  22. Edwards, D. K. and J. T. Bevans, “Radiation Stresses on Real Surfaces,” AIAA Journal, Vol. 3, p. 522–523, 1965.

    Article  Google Scholar 

  23. 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.

    Article  MathSciNet  MATH  Google Scholar 

  24. 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.

    Article  Google Scholar 

  25. 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.

    Google Scholar 

  26. 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.

    Article  Google Scholar 

  27. General Electric Co., Plume and Thrust Tests on Nimbus Attitude Control Nozzles, Information Release 9461–135, May 22, 1964.

    Google Scholar 

  28. 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.

    Google Scholar 

  29. Grubin, C., “Dynamics of a Vehicle Containing Moving Parts,” J. of Applied Mech., Vol. 29, p. 486–488, 1962.

    Article  MATH  Google Scholar 

  30. Hamming, R. W., Numerical Methods for Scientists and Engineers. New York: McGraw-Hill, Inc., 1962.

    MATH  Google Scholar 

  31. Henrici, P. H., Discrete Variable Methods in Ordinary Differential Equations. New York: John Wiley & Sons, Inc., 1962.

    MATH  Google Scholar 

  32. Henrici, P. H., Elements of Numerical Analysis. New York: John Wiley & Sons, Inc., 1964.

    MATH  Google Scholar 

  33. Hildebrand, F. B., Introduction to Numerical Analysis, New York: McGraw-Hill, Inc., 1956.

    MATH  Google Scholar 

  34. 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.

    Article  Google Scholar 

  35. Hooper, L., Private Communication, 1977.

    Google Scholar 

  36. 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.

    Article  MathSciNet  MATH  Google Scholar 

  37. Hultquist, P. F., “Gravitational Torque Impulse on a Stabilized Satellite,” ARS Journal, Vol. 31, p. 1506–1509, 1961.

    MATH  Google Scholar 

  38. 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.

    Google Scholar 

  39. Katz, Paul, “Comments on ‘A Re-Evaluation of Jet Damping’,” J. Spacecraft, Vol. 5, p. 1246, Oct. 1968.

    Article  Google Scholar 

  40. Keat, J. and M. Shear, Apogee Motor Firing Dynamics Study for the Communications Technology Satellite, Comp. Sc. Corp, 3000–05600–08TN, May 1974.

    Google Scholar 

  41. Koelle, H. H., editor, Handbook of Astronautical Engineering. New York: McGraw-Hill Book Co., Inc., 1961.

    Google Scholar 

  42. Lambert. J. D., Computational Methods in Ordinary Differential Equations. New York: John Wiley & Sons, Inc., 1973.

    MATH  Google Scholar 

  43. Langley Research Center, Propellant Slosh Loads, NASA SP-8009, Aug. 1968.

    Google Scholar 

  44. Lawrence, H. R., C. J. Wang, and R. B. Reddy, “Variational Solution of Fuel Sloshing Modes,” Jet Propulsion, Vol. 128, p. 729–736, 1958.

    Google Scholar 

  45. Lomen, D. O., Liquid Propellant Sloshing in Mobile Tanks of Arbitrary Shape, NASA CR-222, April 1965a.

    Google Scholar 

  46. Lomen, D. O., Digital Analysis of Liquid Propellant Sloshing in Mobile Tanks with Rotational Symmetry, NASA CR-230, May 1965b.

    Google Scholar 

  47. Mariner-Mars 1964 Project Report: Mission and Spacecraft Development, vol. I: From Project Inception through Midcourse Maneuver, JPL, Tech. Report 32740, March 1965.

    Google Scholar 

  48. Marshall Space Flight Center, The Meteroid Satellite Project Pegasus, First Summary Report, NASA TN D-3505, 1966.

    Google Scholar 

  49. 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.

    Google Scholar 

  50. 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.

    Google Scholar 

  51. 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.)

    Google Scholar 

  52. 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.

    Article  Google Scholar 

  53. NASA, Application Technology Satellite, Vol. 1–8, Tech. Data Report. GSFC, NASA TM X-61130, 1968.

    Google Scholar 

  54. NASA, Spacecraft Magnetic Torques, NASA SP-8018, March 1969a.

    Google Scholar 

  55. NASA, Spacecraft Radiation Torques, NASA SP-8027, Oct. 1969b.

    Google Scholar 

  56. NASA, Research Center Pioneer Project Office, Pioneer VI Mission, NASA Ames Research Center, Moffet Field, CA, May 22, 1967.

    Google Scholar 

  57. Nidey, R. A., “Gravitational Torque on a Satellite of Arbitrary Shape,” ARS Journal, Vol. 30, p. 203–204, 1960.

    MATH  Google Scholar 

  58. Nidey, R. A., “Secular Gravitational Torque on a Satellite in a Circular Orbit,” ARS Journal, Vol. 31, p. 1032, 1961.

    Google Scholar 

  59. Page, G., Private Communication, Nov. 1975.

    Google Scholar 

  60. Papis, T., “Comments on ‘A Re-Evaluation of Jet Damping’,” J. Spacecraft, Vo. 5, p. 1246–1247, Oct. 1968.

    Article  Google Scholar 

  61. Poli, Corrado R., “Effect of Man’s Motion on the Attitude of a Satellity,” J. Spacecraft, Vol. 4, p. 15–20, 1971.

    Article  Google Scholar 

  62. Ralston, A., A First Course in Numerical Analysis. New York: McGraw-Hill, Inc., 1965.

    MATH  Google Scholar 

  63. Rathayya, J. V., Sloshing of Liquid in Axisymmetric Ellipsoidal Tanks, AIAA Paper No. 65–114, Jan. 1965.

    Google Scholar 

  64. 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.

    MATH  Google Scholar 

  65. Roberson, R. E., “Gravitational Torque on a Satellite Vehicle,” J. Franklin Institute, Vol. 265, p. 13–22, 1958b.

    Article  MathSciNet  MATH  Google Scholar 

  66. Roberson, R. E., “Alternate Form of a Result by Nidey,” ARS Journal, Vol. 31, p. 1292, 1961.

    Google Scholar 

  67. Schaaf, S. A. and P. L. Chambré, Flow of Rarefied Gas. Princeton, N.J.: Princeton University Press, 1961.

    Google Scholar 

  68. Schalkowski, S. and M. Harris, Spacecraft Mass Expulsion Torques, NASA SP-8034, Dec. 1969.

    Google Scholar 

  69. 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.

    Google Scholar 

  70. Tandon, G. K. and P. M. Smith, Communications Technology Satellite (CTS) Postlaunch Report, Comp. Sc. Corp., CSC/TM-76/6104, May 1976.

    Google Scholar 

  71. Thomson, W. T. and Y. C. Fung, “Instability of Spinning Space Stations Due to Crew Motion,” AIAA J., Vol. 3, p. 1082–1087, 1965.

    Article  Google Scholar 

  72. 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.

    Article  Google Scholar 

  73. 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.

    Article  Google Scholar 

  74. Victor, P. T., Initial Stabilization Control Nozzle Plume Impingement Study, General Electric Co., Data Memo 1:57, Oct. 1964.

    Google Scholar 

  75. 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.

    Google Scholar 

  76. Warner, G. C. and V. W. Snyder, “A Re-Evaluation of Jet Damping,” J. Spacecraft, Vol. 5, p. 364–366, March 1968.

    Article  Google Scholar 

  77. 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.

    Google Scholar 

  78. 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.

    Article  MathSciNet  Google Scholar 

  79. Yong, K., NASA Goddard Space Flight Center Sounding Rocket Division, MASS Program Documentation, AVCO Systems Division: Seabrook, MD, Aug. 1974.

    Google Scholar 

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© 1978 D. Reidel Publishing Company, Dordrecht, Holland

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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

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  • 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

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