Geodesic
Vector integrals of the Euler, Poisson and Volterra-Zhukovsky equations
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2022), pp. 62-75

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The dynamic Euler equations for a rotating rigid body with a fixed point in projection on fixed (inertial) axes are derived. A complete system of analytical integrals in the form of a vector integral for the dynamic Euler equation with the zero right side, as well as for the kinematic Poisson and Volterra-Zhukovsky equations is presented. All these integrals do not contain elliptic quadratures.
Mots-clés : Euler equations, Poisson equations, Volterra-Zhukovsky equations, elliptic quadrature.
Keywords: vector integrals, solid dynamics 
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     author = {V. N. Onikiychuk and I. V. Onikiychuk},
     title = {Vector integrals of the {Euler,} {Poisson} and {Volterra-Zhukovsky} equations},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {62--75},
     publisher = {mathdoc},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2022_3_a4/}
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V. N. Onikiychuk; I. V. Onikiychuk. Vector integrals of the Euler, Poisson and Volterra-Zhukovsky equations. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2022), pp. 62-75. http://geodesic.mathdoc.fr/item/VTPMK_2022_3_a4/