Asteroid mean elements: Higher order and iterative theories

Celestial Mechanics and Dynamical Astronomy

Volumn 71, Issue 1, 1998, Pages 55-78

  Milani, Andrea ^b   Knežević, Zoran ^a  

^a Astronomska Opservatorija

^b UNIVERSITY OF PISA   (Italy)

Author keywords

Analytical theories; Asteroids; Iterative methods; Lie series; Mean elements; Mean motion resonances; Runge Kutta; Short periodic perturbations; Themis family

Indexed keywords

EID: 0006841701     PISSN: 09232958     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008315029975     Document Type: Article

References (23)

1. Arnold, V. I.: 1963, 'Small denominators and problems of stability of motion in classical and celestial mechanics', Russian Mathematical Surveys 18, 85-191.
2. Arnold, V. I.: 1976, Les Méthodes mathématiques de la mécanique classique, Éditions MIR, Moscou.
3. Breiter, S.: 1997a, 'On the numerical transformation of variables in perturbation theory', Celest. Mech. Dyn. Astron. 65, 345-354.
4. Breiter, S.: 1997b, 'Second order solution for the zonal problem of satellite theory', Celest. Mech. Dyn. Astron. 67, 237-249.
5. Butcher, J. C.: 1987, The Numerical Analysis of Ordinary Differential Equations, J Wiley.
6. Carpino, M., Milani, A. and Nobili, A. M.: 1987, 'Long-term numerical integrations and synthetic theories for the motion of the outer planets', Astron. Astrophys. 181, 182-194.
7. Cooper, G. J.: 1987, 'Stability of Runge-Kutta methods for trajectory problems', IMA J. Numer. Anal. 7, 1-13.
8. Danby, J. M. A.: 1988, Fundamentals of Celestial Mechanics, Willmann-Bell.
9. Hori, G.: 1966, 'Theory of general perturbations with unspecified canonical variables', Publ. Astron. Soc. Japan 18, 287-296.
10. Knežević, Z.: 1988, 'Asteroid mean orbital elements', Bull. Astron. Obs. Belgrade 139, 1-6.
11. Knežević, Z.: 1992, 'Minor planet short-periodic perturbations: the indirect part of the disturbing function', Celest. Mech. Dyn. Astron. 55, 387-404.
12. Message, P. J.: 1976, 'Formal expressions for the motion of N planets in the plane, with the secular variations included, and an extension to Poisson's theorem', in: Szebehely and Tapley (eds), Long-Time Predictions in Dynamics, Reidel, Dordrecht, Holland, pp. 279-293.
13. Milani, A.: 1988, 'Secular perturbations of planetary orbits and their representation as series', in: A.E. Roy, (ed), Long-term Dynamical Behaviour of Natural and Artificial N-Body Systems, Kluwer Academic Publishers, pp. 73-108.
14. Milani, A., and Knežević, Z.: 1990, 'Secular perturbation theory and computation of asteroid proper elements', Celest. Mech. Dyn. Astron. 49, 347-411 (Paper I).
15. Milani, A., and Knežević, Z.: 1992, 'Asteroid proper elements and secular resonances', Icarus 98, 211-232 (Paper II).
16. Milani, A. and Knežević, Z.: 1994, 'Asteroid proper elements and the dynamical structure of the asteroid main belt', Icarus 107, 219-254 (Paper III).
17. Milani, A. and Mazzini, G.: 1997, Sistemi dinamici, Pisa University Editorial Service.
18. Milani, A., Nobili, A. M. and Carpino, M.: 1987, 'Secular variations of the semimajor axes: theory and experiments', Astron. Astrophys. 172, 265-279.
19. Milani, A., Nobili, A. M. and Knežević, Z.: 1997, 'Stable chaos in the asteroid belt', Icarus 125, 13-31.
20. Morbidelli A., Zappalà, V., Moons, M., Cellino, A. and Gonczi, R.: 1995, 'Asteroid families close to mean motion resonances: dynamical effects and physical implications', Icarus 118, 132-154.
21. Poincaré, H.: 1893, Les Méthodes Nouvelles de la Mécanique Céleste, Vol. II, Gauthier-Villars; reprinted by Blanchard, Paris, 1987.
22. Sanz-Serna, J. M.: 1988, 'Runge-Kutta schemes for Hamiltonian systems', BIT 28, 877-883.
23. Yuasa, M.: 1973, 'Theory of secular perturbations of asteroids including terms of higher order and higher degree', Publ. Astron. Soc. Japan 25, 399-445.