Algebraic integrals of $n$-body problem in $\Bbb R^k$ (in Ukrainian) |
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| Author |
Faculty of Mechanics and Mathematics, Lviv National University
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| Abstract |
The classical $n$-body problem in $\Bbb R^k$ is considered.
The following generalization of Bruns-Painleve result is proved:
every first integral of this Hamiltonian system which is polynomial in impulses is a function
of certain (known) classical integrals --- energy and kinetic momenta of the system.
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| Keywords |
Hamiltonian systems, first integrals, polynomial integrals in impulses, energy integral, kinetic momenta, Bruns-Painlevé theorem
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| DOI |
doi:10.30970/ms.14.1.97-108
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Reference |
1. Bruns H. Über die integrale des Vielkörper-Problems// Acta Math. – 1888. – V.11. – P.25–96.
2. Painlevé P. Mémoire sur les intégrales premières du problème des $n$ corps// Bulletin Astronomique (Paris). -- 1898. -- T.15. -- P.81--117. 3. Forsyth A. R. Theory of differential equations. V.3, Cambridge, 1900. – 437 pp. 4. Пидкуйко С. И., Степин А. М. Полиномиальные интегралы гамильтоновых систем // ДАН СССР. – 1978. – Т.239, №.1. – C.50–53. |
| Pages |
97-108
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| Volume |
14
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| Issue |
1
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| Year |
2000
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| Journal |
Matematychni Studii
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