Numerical stabilization of orbital motion

Celestial Mechanics and Dynamical Astronomy

Volumn 87, Issue 4, 2003, Pages 383-409

  Avdyushev, Victor A ^a  

^a Applied Mathematics and Mechanics Institute   (Russian Federation)

Author keywords

Lyapunov's instability; Numerical integration; Orbital motion; Stabilization

Indexed keywords

EID: 3543072885     PISSN: 09232958     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:CELE.0000006765.54357.a8     Document Type: Article

References (13)

1. Ascher, U. M., Chin, H., Petzold, L. and Reich, S.: 1995, 'Stabilization of constrained mechanical systems with DAEs and invariant manifolds', J. Mech. Struct. Machines 23, 135-138.
2. Baumgarte, J.: 1972, 'Stabilization of constraints and integrals of motion in dynamical systems', Comp. Math. Appl. Mech. Eng. 1, 1-16.
3. Baumgarte, J.: 1973, 'Numerical stabilization of the differential equations of Keplerian motion', Celest. Mech. 5(4), 490-501.
4. Bordovitsyna, T. V. and Sukhoplyueva, L. E.: 1980, 'Research in the efficiency of numerical algorithms using stabilizing transformations', Bull. ITA AS USSR (Leningrad: ITA AS USSR) 10(163), 591-596.
5. Burdet, C. A.: 1968, 'Theory of Kepler motion: the general perturbed two body problem', Z. Angew. Math. Phys. 19, 345-368.
6. Chin, H.: 1995, 'Stabilization Methods for Simulations of Constrained Multibody Dynamics', PhD Thesis, Institute of Applied Mathematics, University of British Columbia, Canada.
7. Everhart, E.: 1974, 'Implicit single sequence methods for integrating orbits', Celest. Mech. 10, 35-55.
8. Jacobson, R. A.: 1994, 'Revised ephemerides of the inner Jovian satellites', JPL IOM 314, 10-101.
9. Lieske, J. H.: 1998, 'Galilean satellites ephemerides E-5', Astron. Astrophys. 129, 205-217.
10. Murison, M. A.: 1989, 'On an efficient and accurate method to integrate restricted three-body orbits', Astron. J. 97(5), 1496-1509.
11. Nacozy, P. E.: 1971, 'The use of integrals in numerical integrations of the N-body problem', Astrophys. Space Sci. 14, 40-51.
12. Rohde, J. R. and Sinclair, A.: 1992, 'Orbital ephemeredes and rings of satellites', Explanatory Supplement to the Astronomical Almanac, 325-381.
13. Stiefel, E. L. and Scheifele, G.: 1971, Linear and Regular Celestial Mechanics, Springer-Verlag, Berlin, Heidelberg, New York.