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Symplectic maps for the n-body problem
Abstract
The present study generalizes the mapping method of Wisdom (1982) to encompass all gravitational n-body problems with a dominant central mass. The rationale for the generalized mapping method is discussed as well as details for the mapping for the n-body problem. Some refinements of the method are considered, and the relationship of the mapping method to other symplectic integration methods is shown. The method is used to compute the evolution of the outer planets for a billion years. The resulting evolution is compared to the 845 million year evolution of the outer planets performed on the Digital Orerry using standard numerical integration techniques. This calculation provides independent numerical confirmation of the result of Sussman and Wisdom (1988) that the motion of the planet Pluto is chaotic.
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Cited by
A hybrid symplectic integrator that permits close encounters between massive bodies
Chambers, J. E. (1999) · Monthly Notices of the Royal Astronomical Society · doi:10.1046/j.1365-8711.1999.02379.x · Cited by 1,820
REBOUND: an open-source multi-purpose N-body code for collisional dynamics
Rein, H., & Liu, S.-F. (2012) · Astronomy & Astrophysics · doi:10.1051/0004-6361/201118085 · Cited by 1,180
Long term evolution and chaotic diffusion of the insolation quantities of Mars
Laskar, J., Correia, A. C. M., Gastineau, M., Joutel, F., Levrard, B., & Robutel, P. (2004) · Icarus · doi:10.1016/j.icarus.2004.04.005 · Cited by 992
The Eccentric Kozai-Lidov Effect and Its Applications
Naoz, S. (2016) · Annual Review of Astronomy and Astrophysics · doi:10.1146/annurev-astro-081915-023315 · Cited by 848
Rein, H., & Spiegel, D. S. (2015) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stu2164 · Cited by 722
Metadata
- Authors
- Wisdom, J., & Holman, M.
- Venue
- The Astronomical Journal
- Publisher
- American Astronomical Society
- Published
- 1991-10
- Volume
- 102
- Pages
- 1528
- ISSN
- 0004-6256 (ISSN-L)
- OpenAlex
- W1976860825
- Cited by
- 1,196
- References
- 0
- FWCI
- 11.49
- Type
- journal article
- Language
- en
- Open access
- closed
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- Wisdom, J., & Holman, M. (1991). Symplectic maps for the n-body problem. The Astronomical Journal. https://doi.org/10.1086/115978
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