Skip to main content
Log in

Multilayer ring structures

  • Published:
Physics of Particles and Nuclei Letters Aims and scope Submit manuscript

Abstract

A study of the behavior of axisymmetric structures is important for understanding the problem of the existence and stability of planet rings, spherical star constellations, and galaxies. The multilayer ring structure algorithm is developed on the basis of an exact solution to the problem of n-body gravitational axisymmetric interaction. As a result of the numerical integration of differential motion equations of point bodies composing the above structures, the evolution of several of their models is investigated. Some of them are invariable in configuration, others change forms due to interlayer interactions, and the rest throw part of bodies out of the structure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. A. Grebenikov, D. Kozak-Skovorodkina, and M. Yakubyak, Computer Algebra Methods in a Many-Body Problem (Ross. Univ. Druzhby Narodov, Moscow, 2002) [in Russian].

    Google Scholar 

  2. E. V. Ikhsanov, The Computer Methods of Hamiltonian Normalization for Restricted Problems of Celestial Mechanics (Ross. Univ. Druzhby Narodov, Moscow, 2002) [in Russian].

    Google Scholar 

  3. N. I. Zemtsova and D. Kozak-Skovorodkina, “Stability Problem of Stationary Solutions of Restricted Problem of 12 Bodies with Incomplete Symmetry in the Case of Frequency Third Order Resonance,” in Theoretical and Applied Problems of Nonlinear Analysis (Vych. Tsentr RAN Dorordnitsyna, Moscow, 2006), pp. 77–90 [in Russian].

    Google Scholar 

  4. E. A. Grebenikov, D. D. Diarova, and N. N. Zemtsova, “Existence and Instability of Diamond-Like Central Configurations in Wintner Sense for Newton Model of 9 Bodies,” in Theoretical and Applied Problems of Nonlinear Analysis (Vych. Tsentr RAN Dorordnitsyna, Moscow, 2006), pp. 65–77 [in Russian].

    Google Scholar 

  5. B. Elmabsout, “Stability of Some Degenerate Positions of Relative Equilibrium in the N-Body Problem,” Dynam. Stabil. Syst. 9, 305–319 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  6. E. A. Grebenikov, “Existence of Precise Symmetric Solutions in Flat Newton Many-Body Problem,” Matem. Model. 10(8), 74–80 (1998).

    MathSciNet  MATH  Google Scholar 

  7. V. D. Gutsu, D. M. Diarova, and N. I. Zemtsova, “Study of Stability of Stationary Solutions of Diamond-Like Restricted 10-Body Problem,” in Theoretical and Applied Problems of Nonlinear Analysis (Vych. Tsentr RAN Dorordnitsyna, Moscow, 2007), pp. 99–109 [in Russian].

    Google Scholar 

  8. I. I. Smul’skii, “Construirovanie kol’tsevykh struktur,” in Fundamental and Applied Problems of Modern Mechanics, Proceedings of the 6th All-Russia Scientific Conference Dedicated to 130 Years of Tomsk State University and 40 Years of Institute of Applied Mathematics and Mechanics of Tomsk State University, Tomsk, 30 Sept.–2 Oct., 2008 (Tomsk, 2008), pp. 431–432.

  9. I. I. Smul’skii, “Axisymmetric Problem of Gravitational Interaction of N-Bodies,” Matem. Model. 15(5), 27–36 (2003), http://www.smul1.newmail.ru/Russian1/IntSun-Syst/Osvnb4.doc.

    MathSciNet  Google Scholar 

  10. I. I. Smul’skii, Interaction Theory (Novosib. Univ., NNTs OIGGM SO RAN, Novosibirsk, 1999) [in Russian], http: // www.ikz.ru/~smulski/TVfulA5-2.pdf.

    MATH  Google Scholar 

  11. E. A. Grebenikov and I. I. Smul’skii, Evolution of the Mars Orbit on Time Span in Hundred Millions Years, Report on Applied Mathematics (Vych. Tsentr RAN Dorodnitsyna, Moscow, 2007) [in Russian], http: // www.ikz.ru/~smulski/Papers/EvMa100m4t2.pdf.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Smul’skii, I.I. Multilayer ring structures. Phys. Part. Nuclei Lett. 8, 436–440 (2011). https://doi.org/10.1134/S1547477111050189

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1547477111050189

Keywords

Navigation