Generating a new recurrence relations system for elliptic Hansen coefficients by means of computer algebra

ABSTRACT

Problem to obtain a new system of recurrence relations for elliptic Hansen coefficients is solved by means of computer algebra system MAPLE. Possibilities for generation of new recurrence relations by means of the MAPLE-package LINALG are shown for the case of linear relations. As an example, advantages to use the obtained recurrence relations in an artificial satellite motion theory within elliptic functions are described.

REFERENCES

• 1: 1. Brumberg E.V. Perturbed two-body motion with elliptic functions. Proc. 25th Symp. on Cel. Mech., NAO, Tokyo, 1992, p. 139.
• 2: 2. Brumberg E.V., Fukushima T. Expansions of elliptic motion based on elliptic function theory. Cel. Mech. and Dyn. Astr., 1993, v. 57.
• 3: 3. Vasiliev N. N., Vakhidov A.A., Sokolsky A.G. Computation of Hamiltonian presenting an artificial Earth satellite motion with large eccentricity. Preprint ITA of Russian Academy of Sciences, 1994, N 38.
• 4: 4. Char B.W., Geddes K.O., Gonnet G.H., Leong B.L., Monagan M.B., Watt S.M. MAPLE V Library Reference Manual, Springer, New York, 1993.
• 5: 5. Vasiliev N.N., Vakhidov A.A., Sokolsky A.G. Computation of Jacobi home functions for a highly elliptic satellite. Proc. Intern. Conf. "Modern Problems of Theoretical Astronomy", St. Petersburg, 1994, v. 1, p. 38.

INDEX TERMS

Primary Classification:
  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Aerospace

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.8 Partial Differential Equations
          Subjects: Elliptic equations

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.3 Languages and Systems

          Nouns: Maple

General Terms:
Experimentation, Performance, Theory

Keywords:
artificial satellites, computer algebra, recurrence relations