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.
CITATION STYLE
Bruno, A. D., & Edneral, V. F. (2012). Calculation of normal forms of the Euler–Poisson equations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7442 LNCS, pp. 60–71). Springer Verlag. https://doi.org/10.1007/978-3-642-32973-9_6
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