Calculation of Normal Forms of the Euler–Poisson Equations
In the paper , 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  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.
KeywordsEuler–Poisson equations resonant normal form computer algebra
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