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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 5, Pages 1063–1100 (Mi izv1927)  

This article is cited in 8 scientific papers (total in 8 papers)

The asymptotic behavior as $N\to\infty$ of the trajectories of $N$ point masses interacting in accordance with Newton's law of gravitation

V. P. Maslov, P. P. Mosolov


Abstract: For systems of particles interacting according to Newton's law of gravitation, the asymptotics of their trajectories are found. It is shown that these asymptotics are connected with the characteristics of Vlasov's equation, describing a collision-free plasma. An estimate of the difference between the trajectories of point masses and the corresponding characteristics of Vlasov's equation is found. It is proved that for small hydrodynamic times the motion of point masses is near to the motion of mass points in a constant field of force, defined by the initial mass distribution (the law of free fall). This law of free fall continues to hold when the particles pass through distances substantially exceeding the initial mutual distances between them.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1979, 13:2, 349–386

Bibliographic databases:

UDC: 517.9
MSC: 70F10, 76X05, 82A45
Received: 04.10.1977

Citation: V. P. Maslov, P. P. Mosolov, “The asymptotic behavior as $N\to\infty$ of the trajectories of $N$ point masses interacting in accordance with Newton's law of gravitation”, Izv. Akad. Nauk SSSR Ser. Mat., 42:5 (1978), 1063–1100; Math. USSR-Izv., 13:2 (1979), 349–386

Citation in format AMSBIB
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\by V.~P.~Maslov, P.~P.~Mosolov
\paper The asymptotic behavior as $N\to\infty$ of the trajectories of~$N$ point masses interacting in accordance with Newton's law of gravitation
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 5
\pages 1063--1100
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=513914}
\zmath{https://zbmath.org/?q=an:0423.70011|0398.70008}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 2
\pages 349--386
\crossref{https://doi.org/10.1070/IM1979v013n02ABEH002047}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JD23800008}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Maslov V., Shvedov O., “A New Asymptotic Method in the Problem of Many Classical Particles”, Dokl. Akad. Nauk, 338:2 (1994), 173–176  mathnet  mathscinet  zmath  isi
    2. V. P. Maslov, “Zeroth-order phase transitions and Zipf law quantization”, Theoret. and Math. Phys., 150:1 (2007), 102–122  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. V. P. Maslov, “General Notion of a Topological Space of Negative Dimension and Quantization of Its Density”, Math. Notes, 81:1 (2007), 140–144  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. V. P. Maslov, “Transition to the Condensate State for Classical Gases and Clusterization”, Math. Notes, 84:6 (2008), 785–813  mathnet  crossref  crossref  mathscinet  isi
    5. V. V. Vedenyapin, M. A. Negmatov, “Derivation and classification of Vlasov-type and magnetohydrodynamics equations: Lagrange identity and Godunov's form”, Theoret. and Math. Phys., 170:3 (2012), 394–405  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    6. V. V. Vedenyapin, M. A. Negmatov, “On derivation and classification of Vlasov type equations and equations of magnetohydrodynamics. The Lagrange identity, the Godunov form, and critical mass”, Journal of Mathematical Sciences, 202:5 (2014), 769–782  mathnet  crossref
    7. Vedenyapin V.V., Negmatov M.A., “On the Topology of Steady-State Solutions of Hydrodynamic and Vortex Consequences of the Vlasov Equation and the Hamilton–Jacobi Method”, Dokl. Math., 87:2 (2013), 240–244  crossref  mathscinet  zmath  isi
    8. V. V. Vedenyapin, M. A. Negmatov, N. N. Fimin, “Vlasov-type and Liouville-type equations, their microscopic, energetic and hydrodynamical consequences”, Izv. Math., 81:3 (2017), 505–541  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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