Studying the stability of the second order non-autonomous hamiltonian system

  • Authors:

  • Evgenii A. Grebenikov;Ersain V. Ikhsanov;Alexander N. Prokopenya

  • Affiliations:

  • Dorodnicyn Computing Center of RAS, Moscow, Russia;Engineer-Humane Institute, Atyrau, Kazakhstan;Brest State Technical University, Brest, Belarus

  • Venue:
  • CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
  • Year:
  • 2007

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Abstract

The problem of studying the stability of equilibrium solution of the second order non-autonomous Hamiltonian system, containing a small parameter, is considered. The main steps in solving this problem and application of the computer algebra systems for doing necessary calculations are discussed. As an example, we analyze stability of some equilibrium solutions in the elliptic restricted (2n + 1)-body problem. The problem is solved in a strict nonlinear formulation. All calculations are done with the computer algebra system Mathematica.