Journal
ACTA MECHANICA
Volume 230, Issue 3, Pages 871-883Publisher
SPRINGER WIEN
DOI: 10.1007/s00707-018-2328-7
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Funding
- RUDN University Program 5-100
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In this paper, we proceed to develop a new approach which was formulated first in Ershkov (Acta Mech 228(7):2719-2723, 2017) for solving Poisson equations: a new type of the solving procedure for Euler-Poisson equations (rigid body rotation over the fixed point) is suggested in the current research. Meanwhile, the Euler-Poisson system of equations has been successfully explored for the existence of analytical solutions. As the main result, a new ansatz is suggested for solving Euler-Poisson equations: the Euler-Poisson equations are reduced to a system of three nonlinear ordinary differential equations of first order in regard to three functions Omega(i) (i = 1,2,3); the proper elegant approximate solution has been obtained as a set of quasi-periodic cycles via re-inversing the proper elliptical integral. So the system of Euler-Poisson equations is proved to have analytical solutions (in quadratures) only in classical simplifying cases: (1) Lagrange's case, or (2) Kovalevskaya's case or (3) Euler's case or other well-known but particular cases.
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