Satellite Dynamics pp 170-179 | Cite as

# Literal Algebra for Satellite Dynamics

## Abstract

Analytical developments of a satellite perturbation theory can be accomplished quickly, accurately, and with generality by use of computer algebra. The basic principles of computer algebra, the required and desirable features of computer-algebra programs, and the applications of computer algebra to specific problems in perturbation analysis will be presented here. The emphasis of non numeric mathematics in computer science, its implications for satellite theory, and the relation of the tool (computer algebra) to the problem (perturbation analysis) will be discussed. The use of computer algebra changes one’s approach to perturbation theory, eliminating one class of problems (e.g., algebraic blunders) while introducing another (e.g., programing mistakes). Larger problems can be solved quickly; however, careful verification is still necessary. The development of computer science is oriented toward question solvability; uniqueness and large problems (efficiency) are not of interest. Conversely, perturbation theory benefits from the automated treatment of long series.

## Keywords

Computer Algebra Perturbation Analysis Celestial Mechanic Satellite Perturbation Algebra Program## Preview

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## References

- 1.Barton, D.; Fitch, J.P.: Applications of algebraic manipulation program in physics. Rep. Prog. Phys. 35 (1972) 235–314.CrossRefGoogle Scholar
- 2.Broucke, R.: Construction of rational and negative powers of a formal series. Comm. ACM 14 (1971) 32–35.zbMATHCrossRefGoogle Scholar
- 3.Cherniack, J.R.: A more general system for Poisson Series manipulation. Celestial Mech. 7 (1973) 107–121.CrossRefGoogle Scholar
- 4.Danby, J.M.A.; Deprit, A.; Rom, A.: The symbolic manipulation of Poisson Series. Math Note No. 432, Document Dl-82–0481, Boeing Sci. Res. Lab. 1965.Google Scholar
- 5.Davis, M.S.: Review of non-numerical uses of computers. In “Recent Advances in Dynamical Astronomy. Ed. by B.D. Tapley and V. Szebehely. Dordrecht-Holland: D. Reidel Pub. Co. 1973, pp. 351–391.CrossRefGoogle Scholar
- 6.Herget, P.; Musen, P.: Astron. J. 64 (1959) 11–20.CrossRefGoogle Scholar
- 7.Jeffreys, W.H.: Automated algebraic manipulation in celestial mechanics. Comm. ACM 14 (1971) 538–541.CrossRefGoogle Scholar