A Riccati-type solution of Euler-Poisson equations of rigid body rotation over the fixed pointстатья
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Дата последнего поиска статьи во внешних источниках: 30 апреля 2021 г.
Аннотация:A new approach is developed here for resolving of the Poisson equations in case the components of angular velocity of rigid body rotation could be considered as the functions of time-parameter t only. Fundamental solution is presented by the analytical formulae in dependence on two time-dependent, the real-valued coefficients. Such coefficients as above are proved to be the solutions of mutual system of 2 Riccati ordinary differential equations (which has no analytical solution in general case). All in all, the cases of analytical resolving of Poisson equation are quite rare (according to the cases of exact resolving of the aforementioned system of Riccati ODEs). So, the system of Euler-Poisson equations is proved to have the 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 (where the existence of particular solutions depends on the choosing of the appropriate initial conditions).