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Calculation of Normal Forms of the Euler–Poisson Equations

  • Alexander D. Bruno
  • Victor F. Edneral
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7442)

Abstract

In the paper [1], the special case of the Euler–Poisson equations describing movements of a heavy rigid body with a fixed point is considered. Among stationary points of the system, two of one-parameter families were chosen. These families correspond to the resonance of eigenvalues (0, 0, λ, − λ, 2λ, − 2λ) of the matrix of the linear part of the system, also in [1] it was conjectured the absence of the additional first integral (with respect to well-known 3 integrals (2)) near these families, except of classical cases of global integrability. In this paper, the supposition is proved by calculations of coefficients of the normal form.

Keywords

Euler–Poisson equations resonant normal form computer algebra 

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alexander D. Bruno
    • 1
  • Victor F. Edneral
    • 2
  1. 1.Keldysh Institute for Applied Mathematics of RASMoscowRussia
  2. 2.Skobeltsyn Institute of Nuclear PhysicsLomonosov Moscow State UniversityMoscowRussia

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