Skip to main content
Log in

Automatic Rendering of Astrodynamics Expressions for Efficient Evaluation

  • Original Article
  • Published:
The Journal of the Astronautical Sciences Aims and scope Submit manuscript

Abstract

In this paper, we describe the automatic rendering of expressions computed using symbolic manipulation. Computations from astrodynamics frequently can be put in a fixed hierarchy of polynomials and Fourier series. Once in this form, FORTRAN subprograms can be generated automatically in a form that lends itself to numerical evaluation. The goal of the current work is to present an approach for using symbolic manipulation techniques to produce a Fortran representation of the normalized Hamiltonian and other supporting equations representing as many of the actual physical effects on satellites as possible.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. BROUWER, D. “Solution to the Problem of Artificial Satellite Theory without Drag,” Astronomical Journal, Vol. 64, 1959, pp. 378–397.

    Article  MathSciNet  Google Scholar 

  2. COFFEY, S.L., NEAL, H.L., SEGERMAN, A.M., and TRAVISANO, J.J. “An Analytic Orbit Propagation Program for Satellite Catalog Maintenance,” AAS Paper 95-426, AAS/AIAA Astrodynamics Specialist Conference, Halifax, Nova Scotia, August 1995.

  3. DEPRIT, A. “The Elimination of the Parallax in Satellite Theory,” Celestial Mechanics, Vol. 24, No. 2, 1981, pp. 111–153.

    Article  MathSciNet  Google Scholar 

  4. STEELE, JR., G.L. Common Lisp, the Language, Digital Press, 1990.

  5. ECKERT, W.J., WALKER, M. J., and ECKERT, D. “Transformations of the Lunar Coordinates and Orbital Parameters,” Astronomical Journal, Vol. 71, No. 5, 1966, pp. 314–332.

    Article  Google Scholar 

  6. COFFEY, S. L., and DEPRIT, A. “Fast Evaluation of Fourier Series,” Astronomy and Astrophysics, Vol. 81, No. 3, 1980, pp. 310–315.

    Google Scholar 

  7. MILLER, B. R. “A Program Generator for Efficient Evaluation of Fourier Series,” Proceedings of ACM-SIGSAM, International Symposium on Symbolic and Algebraic Computation, Portland, Oregon, July 1989, pp. 199–206.

  8. GATES, B. L. “GENTRAN: An Automatic Code Generation Facility for REDUCE,” SIGSAM Bulletin, Vol. 19, No. 3, 1985, pp. 24–42.

    Article  Google Scholar 

  9. GATES, B. L., and VAN HULZEN, J. A. “Automatic Generation of Optimized Programs,” European Conference on Computer Algebra, Linz, Austria, April 1985, pp. 583–584.

    Google Scholar 

  10. COFFEY, S.L., DEPRIT, A., DEPRIT, E., HEALY, L.M., and MILLER, B.R. “A Toolbox for Nonlinear Dynamics,” Computer Aided Proofs in Analysis, Springer-Verlag, New York, 1991, pp. 97–115.

    Book  Google Scholar 

  11. DEPRIT, A. “Canonical Transformations Depending on a Small Parameter,” Celestial Mechanics, Vol. 1, No. 1, 1969, pp. 12–30.

    Article  MathSciNet  Google Scholar 

  12. ABELSON, H., HALIFANT, M., KATZENELSON, J., and SUSSMAN, G.J. “The LISP Experience,” Annual Review of Computer Science, Annual Reviews, Inc., Palo Alto, California, 1988, pp. 167–195.

    Google Scholar 

  13. American National Standard Programming Language FORTRAN, American National Standards Institute, ANSI X3.9-1978, April 1978.

    Google Scholar 

  14. ADAMS, J.C., BRAINERD, W.S., MARTIN, J. T., SMITH, B.T., and WAGENER, J. L. Fortran 90 Handbook: Complete ANSI/ISO Reference, Intertext Publications, McGraw-Hill, New York, 1992.

    Google Scholar 

  15. Connection Machine Fortran Programming Guide and CM Fortran Reference Manual, Thinking Machines Corporation, Cambridge, Massachusetts, 1991.

    Google Scholar 

  16. KOELBEL, C. H., LOVEMAN, D. B., SCHREIBER, R. S., STEELE JR., G. L., and ZOSEL, M. E. The High Performance Fortran Handbook, MIT Press, Cambridge, Massachusetts, 1994.

    Book  Google Scholar 

  17. KNUTH, D.E. Seminumerical Algorithms, Addison-Wesley, Reading, Massachusetts, 1981.

    MATH  Google Scholar 

  18. AHO, A. V., SETHI, R., and ULLMAN, J.D. Compilers Principles, Techniques, Tools, Addison-Wesley, Reading, Massachusetts, 1986.

    MATH  Google Scholar 

  19. WINSTON, P. H., and HORN, B. K. P. LISP, Addison-Wesley, Reading, Massachusetts, 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

work completed while employed by AlliedSignal Corporation at the Naval Research Laboratory

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Healy, L.M., Travisano, J.J. Automatic Rendering of Astrodynamics Expressions for Efficient Evaluation. J of Astronaut Sci 46, 65–81 (1998). https://doi.org/10.1007/BF03546193

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03546193

Navigation