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Nelin. Dinam., 2006, Volume 2, Number 3, Pages 279–285 (Mi nd169)  

This article is cited in 3 scientific papers (total in 3 papers)

Reduction in the two-body problem on the Lobatchevsky plane

A. V. Borisovab, I. S. Mamaevab

a Udmurt State University
b Institute of Computer Science

Abstract: We present a reduction-of-order procedure in the problem of motion of two bodies on the Lobatchevsky plane $\mathbb H^2$. The bodies interact with a potential that depends only on the distance between the bodies (this holds for an analog of the Newtonian potential). In earlier works, this reduction procedure was used to analyze the motion of two bodies on the sphere.

Keywords: Lobatchevsky plane, first integral, reduction-of-order procedure, potential of interaction.

Full text: PDF file (277 kB)

Document Type: Article
UDC: 521.1

Citation: A. V. Borisov, I. S. Mamaev, “Reduction in the two-body problem on the Lobatchevsky plane”, Nelin. Dinam., 2:3 (2006), 279–285

Citation in format AMSBIB
\Bibitem{BorMam06}
\by A.~V.~Borisov, I.~S.~Mamaev
\paper Reduction in the two-body problem on the Lobatchevsky plane
\jour Nelin. Dinam.
\yr 2006
\vol 2
\issue 3
\pages 279--285
\mathnet{http://mi.mathnet.ru/nd169}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Burov, “On the motion of a solid body on spherical surfaces”, Journal of Mathematical Sciences, 199:5 (2014), 501–509  mathnet  crossref  mathscinet
    2. Alexey V. Borisov, Ivan S. Mamaev, “Symmetries and Reduction in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 20:5 (2015), 553–604  mathnet  crossref  mathscinet  zmath
    3. Garcia-Naranjo L.C., Marrero J.C., Perez-Chavela E., Rodriguez-Olmos M., “Classification and Stability of Relative Equilibria For the Two-Body Problem in the Hyperbolic Space of Dimension 2”, J. Differ. Equ., 260:7 (2016), 6375–6404  crossref  isi
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