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Simulation of the algorithms and their visualization forthe solutions to the restricted problems of the cosmic dynamics of the fourteen bodies with three rings

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Języki publikacji
EN
Abstrakty
EN
The restricted problem of the fourteen bodies with three rings is considered. The results of the visualization and dynamic investigations with the Mathematica system are given. The equilibrium positions are found with the use of analytical, numerical and graphical possibilities of the system. The stability of the equilibrium positions is then considered. Visualization and animation techniques are used for the observations of the motion processes.
Rocznik
Strony
55--65
Opis fizyczny
Bibliogr. 17 poz., rys.
Twórcy
autor
  • The John Paul II Catholic University of Lublin, Department of Mathematical and Natural Sciences, Institute of Mathematics and Computer Science,ul. Konstantynow 1H, 20-708 Lublin, Poland
Bibliografia
  • [1] Poincaré H., Les méthodes nouvelles de la mécanique céleste. Paris. Gauthier-Villars t. I (1882), t. II (1894).
  • [2] Elmabsout B., Sur l’existence de certaines configurations d’equillibre relatif dans le probleme des corps, Celestial Mechanics and Dynamical Astronomy 41 (1988): 131.
  • [3] Grebenicov E., New exact solutions in the planar, symmetrical -body problem, Rom. Astron. J. 7(2) (1998): 151.
  • [4] Grebenicov E., Two New Dynamical Models in Celestial Mechanics, Rom. Astron. J. 8(1) (1998): 13.
  • [5] Grebenikov E.A., Gadomski L.J., The Existence Conditions for Equilibriums In a Bounded Circular Many-Body Problem, Proceedings of Steklov Institute of Mathematics 223 (1998): 159.
  • [6] Jakubiak M., Sufficient Conditions of Linear Stability for Equilibrium Points in the Newtonian Gravitational Model of Six Bodies, -Kiev: Nonlinear Oscillations 2(1) (1999): 138.
  • [7] Grebenikov E.A., Kozak-Skoworodkin D., Jakubiak M., Methods of Computer Algebra in Many-Body Problem, – Moscow: Ed. of UFP (2002): 209.
  • [8] Wolfram Web Resources [Electronic resource] / ed. S. Wolfram. – Champaign (2011) – Mode of access: www.wolfram.com.
  • [9] Gadomski L.J., Grebenikov E.A., Jakubiak M., Kozak-Skoworodkin D., The Lyapunov Stability in Restricted Problems of Cosmic Dynamics, Buletinul Academiei de Stinte a Republicii Moldova. Matematica 1(41) (2003).
  • [10] Siluszyk A., On the linear stability of relative equilibria in the restricted eight-body problem with partial symmetry, Herald of Brest State University, Series I (Math., Phys., Chem., Biol.) 2 (2004): 20.
  • [11] Ikhsanov E. V., Normalization computer methods of hamiltonians for restricted cosmic dynamics problems, Moscow: Ed. of UFP (2004): 132.
  • [12] Kozak-Skoworodkin D., The Qualytative Researches of Many Body Newtonian Problem by Mathematica System, Moscow, Ed. of UFP (2005): 146.
  • [13] Gadomski L., Kovalchuk I.R., Chichurin A.V., The construction of the mathematical models for the cosmic dynamics problems in the Mathematica computer algebra system, Moscow State University’s Press Publishers (2007): 112.
  • [14] Gadomski L., Chichurin A.V., Animation of graphical information in the restricted fourteen body problem with the incomplete symmetry, Herald of Brest State University, Series I (Math., Phys., Chem., Biol.) 1(32) (2009): 17.
  • [15] Chichurin A.V., Numerical studies of the restricted Newton problem with the incomplete symmetry, Collected works of the Institute of System Analysis of the Russian Academy of Sciences 32 (3) (2008): 210.
  • [16] Bang D., Elmabsout B., Configurations polygonales en equilibre relative, Paris: C.R. Acad. Sci., Serie II b 329 (2001): 243.
  • [17] Moser J.K., Lectures on Hamiltonian Systems, – New York, Courant Institute of Mathematical Science (1968): 295.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-46630ba0-55ee-4260-b446-1d9aea9c4989
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