Certificate of Registration Media number Эл #ФС77-53688 of 17 April 2013. ISSN 2308-6033. DOI 10.18698/2308-6033
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New integrable cases in the problem of a rigid body motion in ideal incompressible fluid

Published: 05.03.2014

Authors: Pleshakov Yu.D.

Published in issue: #1(25)/2014

DOI: 10.18698/2308-6033-2014-1-1188

Category: Engineering Sciences | Chapter: Theoretical Mechanics. Design of mechanisms and machines

The paper considers the classical problem of motion of a rigid body in a multivariable ideal incompressible fluid - Kirchhoff problem. The study shows that in the case when the parameters of the Hamiltonian matrix are reduced to a diagonal form, the elements of diagonal matrices have no restrictions, namely, all the 9 parameters are independent and can take any value. It is shown that by using canonical transformations, equations of motion in an axisymmetric spherical force field are reduced to the form of Kirchhoff s equations describing the motion of a rigid body in a multivariable ideal incompressible fluid. It is stressed that the equations of the problem are integrated in quadratures with an arbitrary tensor of inertia, arbitrary location of the masses center and arbitrary quadratic part of the potential. Classical integrable Lagrange, Kovalevskaya, Goryachev-Chaplygin’s cases are included in the found solution as a partial result.

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