NBI

Numerical integrators for the gravitational N-body problem

This code was developed by F. Varadi in collaboration with M. Ghil, W. I. Newman, W. M. Kaula, K. Grazier, D. Goldstein and M. Lessnick. The partial financial support of NSF Grants ATM95-23787 (M. Ghil and F. Varadi) and AST96-19574 (F. Varadi and W. M. Kaula) is gratefully acknowledged.

Description

Four numerical integrators for the gravitational (nonrelativistic) N-body problem are bundled into a single source code. The N bodies are assumed to be point masses. Particles with zero mass are called test particles and they are assumed not to influence each other and the particles with nonzero mass.

The integrators are:

a) A Wisdom-Holman-type mapping for hierarchical N-body systems. This can deal with more general arrangements than the standard Wisdom-Holman mapping such as hierarchical N-body systems (Roy, 1988). The integrator takes advantage of certain properties of symplectic forms and Jacobi coordinates, these are described in Varadi et al., 1998, Mass-Weighted Symplectic Forms for the N-Body Problem (access the local PDF file or PDF file from the publisher). We also use singularly weighted symplectic forms, these are discussed in depth by Varadi et al., Singularly Weighted Symplectic Forms and Applications to Asteroid Motion (1995).

b) A modified Cowell-Stormer integrator, with modifications by W. I. Newman and his students.

c) A Gragg-Bulirsch-Stoer integrator, as it is described by Hairer et al., (1993).

d) A symplectic mapping with Kinetic-Potential energy splitting. This is included for the sake of completeness.

The code is written in standard C. It can be compiled with a single command and should run on all platforms.

More information is provided in the code.

  • Click here for the code.
    Size: 60 Kb, about 1800 lines.

  • Click here for a sample input file.
    Method: Hierarchical Wisdom-Holman mapping.

  • Click here for another sample input file.
    Method: Cowell-Stormer integartor.

    References

    Goldstein, D.: 1996, The Near-Optimality of Stormer Methods for Long Time Integrations of y''=g(y), Ph.D. Dissertation, Univ. of California, Los Angeles, Dept. of Mathematics

    Hairer, E., Norsett, S. P. and Wanner, G.: 1993, Solving Ordinary Differential Equations I. Nonstiff Problems. Second Revised Edition, Springer-Verlag

    Lessnick, M.: 1996, Stability Analysis of Symplectic Integration Schemes, Ph.D. Dissertation, Univ. of California, Los Angeles, Dept. of Mathematics

    Roy, A. E.: 1988, Orbital Motion, Institute of Physics Publishing, Bristol

    Varadi, F. De la Barre, Kaula, W. M. and Ghil, M.: 1995, Singularly Weighted Symplectic Forms and Applications to Asteroid Motion, Celestial Mechanics and Dynamical Astronomy, vol. 62, pp. 23-41

    Varadi, F., M. Ghil and W. M. Kaula: 1999, Mass-Weighted Symplectic Forms for the N-body Problem, Celestial Mechanics and Dynamical Astronomy, vol. 72, pp. 187-199

    Yoshida, H.: 1993, Recent Progress in the Theory and Application of Symplectic Integrators, Celestial Mechanics and Dynamical Astronomy, vol. 56, pp. 27-43

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