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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
1998
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/9805088 |
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| _version_ | 1866909853518135296 |
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| author | Henon, M. Petit, J-M. |
| author_facet | Henon, M. Petit, J-M. |
| contents | Numerical integrations in celestial mechanics often involve the repeated computation of a rotation with a constant angle. A direct evaluation of these rotations yields a linear drift of the distance to the origin. This is due to roundoff in the representation of the sine s and cosine c of the angle theta. In a computer, one generally gets c^2 + s^2 <> 1, resulting in a mapping that is slightly contracting or expanding. In the present paper we present a method to find pairs of representable real numbers s and c such that c^2 + s^2 is as close to 1 as possible. We show that this results in a drastic decrease of the systematic error, making it negligible compared to the random error of other operations. We also verify that this approach gives good results in a realistic celestial mechanics integration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_9805088 |
| institution | arXiv |
| publishDate | 1998 |
| record_format | arxiv |
| spellingShingle | Good rotations Henon, M. Petit, J-M. Numerical Analysis 65G05 (Primary) 70F15 (Secondary) Numerical integrations in celestial mechanics often involve the repeated computation of a rotation with a constant angle. A direct evaluation of these rotations yields a linear drift of the distance to the origin. This is due to roundoff in the representation of the sine s and cosine c of the angle theta. In a computer, one generally gets c^2 + s^2 <> 1, resulting in a mapping that is slightly contracting or expanding. In the present paper we present a method to find pairs of representable real numbers s and c such that c^2 + s^2 is as close to 1 as possible. We show that this results in a drastic decrease of the systematic error, making it negligible compared to the random error of other operations. We also verify that this approach gives good results in a realistic celestial mechanics integration. |
| title | Good rotations |
| topic | Numerical Analysis 65G05 (Primary) 70F15 (Secondary) |
| url | https://arxiv.org/abs/math/9805088 |