On integrable three-body problems on the line |
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| Author |
Department of Mechanics and Mathematics, Lviv University
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| Abstract |
The natural systems of three pair-interacting particles on the line are
investigated. The properties of
interactive potentials are considered under assumption that the given
system has
the first integral which is a polynomial of prescribed degree in the
momenta. The functional equations for those potentials are obtained.
All such potentials for special functional classes are described.
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| Keywords |
three pair-interacting particles, natural systems, interaction potentials, first integral, polynomial in momenta, functional equations
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| DOI |
doi:10.30970/ms.10.1.97-102
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Reference |
1. Moser J. Three integrable Hamiltonian systems connected with semisimple Lie algebras// Invent. Math.--1976 V.37 №2 p.93–108
2. Calogero F Exactly solvable one-dimensional many body problems// Letters al Nuovo Cimento–1975 V.13 №11 p.411–416 3. Pidkuiko S.I., Stepin A.M. Polynomial integrals of Hamiltonian systems// Dokl. Akad. Nauk SSSR–1978V.239№1p.50–51 English transl. in Soviet Math. Dokl. 19. (1978), no.2, 282–286 4. Yoshida H. A criterion for the non-existence of an additional analytic integral in Hamiltonian systems with $n$ degrees of freedom// Phys.Lett.A. -- 1989 V.141 №3 -- 4 p.108--112 |
| Pages |
97-102
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| Volume |
10
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| Issue |
1
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| Year |
1998
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| Journal |
Matematychni Studii
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| Full text of paper | |
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