Numerical Study of Stability Domains of Hamiltonian Equation Solutions

  • E. A. Grebenicov
  • D. Kozak-Skoworodkin
  • D. M. Diarova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4194)


The computer algebra methods are effective means for the search of approximate and exact solutions of differential equations of theoretical physics, celestial mechanics, astrodynamics, and other natural sciences. Before appearance of Programming Systems such as Mathematica, Maple etc., we knew for classical Newtonian three-body problem only Euler exact collinear and Lagrange triangular solutions, for many-body problem – the rotating regular tetragon solution found by A. Dziobek [1] and the general homographic solution theory developed by A. Winter [2] in the 30es of the 20th century. An amount of similar research [3,4,5,6,7,8,9,10] has grown recently due to the fact that the existence of central configurations of the many-body problem is eventually reduced to the solution of the systems of nonlinear algebraic-irrational equations, which can be solved only by the computer algebra methods, thanks to exceptional properties of them.


Equilibrium Position Computer Algebra Interpolation Function Celestial Mechanic Stability Domain 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • E. A. Grebenicov
    • 1
  • D. Kozak-Skoworodkin
    • 2
  • D. M. Diarova
    • 3
  1. 1.Computing Center of RASMoscow
  2. 2.University of PodlasiePoland
  3. 3.Institute of Oil and GasAtyrauKazakhstan

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