The Disturbing Function in Solar System Dynamics

Icarus

Volumn 147, Issue 1, 2000, Pages 129-144

  Ellis, Keren M ^a   Murray, Carl D ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Celestial mechanics; Orbits; Resonances

Indexed keywords

EID: 0142118115     PISSN: 00191035     EISSN: None     Source Type: Journal    
DOI: 10.1006/icar.2000.6399     Document Type: Article

References (31)

1. Allan R. R. Evolution of the Mimas-Tethys commensurability. Astron. J. 74:1969;497-506.
2. Allan R. R. On the evolution of commensurabilities between natural satellites. Symposia Mathematica III. 1970.
3. Boquet F. Développement de la fonction perturbatrice, calcul des terms du huitième ordre. Ann. Obs. Paris, Mém. 19:1889.
4. Broucke R., Smith G. Expansion of the planetary disturbing function. Celest. Mech. 4:1971;490-499.
5. Brouwer D., Clemence G. M. Methods of Celestial Mechanics. 1961.
6. Brown E. W., Shook C. A. Planetary Theory. 1933.
7. Brumberg V. A. Analytical Techniques of Celestial Mechanics. 1995.
8. Deprit A., Henrard J., Rom A. Analytical lunar ephemeris: Delaunay's theory. Astron. J. 76:1971;269-272.
9. Dermott S. F., Murray C. D. Nature of the Kirkwood gaps in the asteroid belt. Nature. 301:1983;201-205.
10. Goldreich P., Nicholson P. D. The revenge of tiny Miranda. Nature. 269:1977;783-785.
11. Hamilton D. P. A comparison of Lorentz, planetary gravitational, and satellite gravitational resonances. Icarus. 109:1994;221-240.
12. Harper, D., and C. D. Murray1994. Disturbing function expansions. Special issue of the Maple Tech. Newsl.December 1994, 24-28.
13. Henrard J. A survey of Poisson series processors. Celest. Mech. 45:1989;245-253.
14. Hughes S. The computation of tables of Hansen coefficients. Celest. Mech. 25:1981;101-107.
15. Jarnagin M. P. Expansions in elliptical motion. Astron. Pap. Am. Ephem. Naut. Alm. 18:1965;1-659.
16. Kaula W. M. Development of the lunar and solar disturbing functions for a close satellite. Astron. J. 67:1962;300-303.
17. Laskar, J.1991. Analytical framework in Poincaré variables for the motion of the solar system. In Predictability, Stability, and Chaos in N-Body Dynamical SystemsA. E. Roy, Ed., pp. 93-114. Plenum Press, New York.
18. Le Verrier U. J.-J. Développment de la fonction qui sert de base au calcul des perturbations des mouvements des planètes. Ann. Obs. Paris, Mém. 1:1855;258-331.
19. Message P. J. On the second order long-period motion of Hyperion. Celest. Mech. Dyn. Astron. 56:1993;277-284.
20. Murray C. D. Nodal regression of the Quadrantid meteor stream: An analytical approach. Icarus. 49:1982;125-134.
21. Murray C. D. A note on Leverrier's expansion of the disturbing function. Celest. Mech. 36:1985;163-164.
22. Murray C. D. The structure of the 2:1 and 3:2 jovian resonances. Icarus. 65:1986;70-82.
23. Murray C. D., Dermott S. F. Solar System Dynamics. 1999.
24. Murray C. D., Harper D. Expansion of the planetary disturbing function to eighth order in the individual orbital elements. QMW Maths Notes. 15:1993.
25. Newcomb S. A development of the perturbative function in cosines of multiples of the mean anomalies and of angles between the perihelia and common node and in powers of the eccentricities and mutual inclination. Astron. Papers Am. Ephem. 5:1895;5-48.
26. Norén G., Wallberg J. A. Entwickelung der störunsfunktion durch kanonische elemente. Öfversigt af Kongl. Vetens-Akad. Forhandlingar. 9:1899;941-961.
27. Peirce B. Development of the perturbative function of planetary motion. Astron. J. 1:1849;1-8.
28. Plummer H. C. An Introductory Treatise on Dynamical Astronomy. 1918.
29. Šidlichovský M., Melendo B. Mapping for 5/2 asteroidal commensurability. Bull. Astron. Inst. Czechosl. 37:1986;65-80.
30. Wisdom J. The origin of the Kirkwood gaps: A mapping technique for asteroidal motion near the 3/1 commensurability. Astron. J. 87:1982;577-593.
31. Wolfram S. Mathematica. A System for Doing Mathematics by Computer. 1991.