| Title:
|
An alternative proof of Painlevé's theorem (English) |
| Author:
|
Němec, Jan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
291-299 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article we show some aspects of analytical and numerical solution of the $n$-body problem, which arises from the classical Newtonian model for gravitation attraction. We prove the non-existence of stationary solutions and give an alternative proof for Painlevé’s theorem. (English) |
| Keyword:
|
$n$-body problem |
| Keyword:
|
ordinary differential equations |
| Keyword:
|
Painlevé’s theorem |
| MSC:
|
70F10 |
| MSC:
|
70F16 |
| idZBL:
|
Zbl 1058.70015 |
| idMR:
|
MR1763173 |
| DOI:
|
10.1023/A:1022371412511 |
| . |
| Date available:
|
2009-09-22T18:03:59Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134440 |
| . |
| Reference:
|
[1] P. Andrle: Foundation of Celestial Mechanics.Academia, Praha, 1971. (Czech) |
| Reference:
|
[2] P. Andrle: Celestial Mechanics.Academia, Praha, 1987. (Czech) |
| Reference:
|
[3] J. Kofroň: Ordinary Differential Equations in Real Space.Univerzita Karlova, Praha, 1990. (Czech) |
| Reference:
|
[4] M. Křížek: On the three-body problem.Rozhledy mat.-fyz. 70 (1992), 105–112. (Czech) |
| Reference:
|
[5] M. Křížek: Numerical experience with the three-body problem.Comput. Appl. Math. 63 (1995), 403–409. MR 1365579, 10.1016/0377-0427(95)00067-4 |
| Reference:
|
[6] M. Křížek: Numerical experience with the finite speed of gravitational influence.Math. Comput. Simulation 50 (1999), 237–245. MR 1717610, 10.1016/S0378-4754(99)00085-3 |
| Reference:
|
[7] J. Kurzweil: Ordinary Differential Equations.Elsevier, Amsterdam, 1986. Zbl 0667.34002, MR 0929466 |
| Reference:
|
[8] Ch. Marchal: The Three Body Problem.Elsevier, Amsterdam, 1990. Zbl 0719.70006, MR 1124619 |
| Reference:
|
[9] A. Marciniak: Numerical Solution of the $N$-Body Problem.Reidel Publishing Company, Dordrecht, 1985. MR 0808778 |
| Reference:
|
[10] P. Painlevé: Leçons sur la Théorie Analytic des Equations Différentielles.Hermann, Paris, 1897. |
| Reference:
|
[11] D. G. Saari, Z. Xia: Off to infinity in finite time.Notices Amer. Math. Soc. 42 (1995), 538–546. MR 1324734 |
| . |
