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Ukraine Donetsk
Year
2019
Volume
29
Issue
1
Pages
73-83
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Section Mechanics
Title On generalized N. Kovalevski equations in two problems of rigid body dynamics
Author(-s) Zyza A.V.a
Affiliations Donetsk National Universitya
Abstract In this paper we consider the reduction of Kirchhoff-Poisson equations related to the problem of rigid body motion under the action of potential and gyroscopic forces and also equations of the problem of rigid body motion taking into account the Barnett-London effect. For the above-mentioned problems, we obtain analogues of N. Kovalevski equations. In addition, for the above-mentioned problems we obtain two new particular solutions to the polynomial class of Steklov-Kovalevski-Goryachev reduced differential equations. The polynomial solution of the problem of gyrostat motion under the action of potential and gyroscopic forces is characterized by the following property: the squares of the second and the third vector component of angular velocity are quadratic polynomials of the first vector component that is an elliptic function of time. A polynomial solution of the equation of rigid body motion in a magnetic field (taking into account the Barnett-London effect) is characterized by the fact that the square of the second vector component of the angular velocity is the second-degree polynomial, while the square of the third component is the fourth-degree polynomial of the first vector component. The former is found as a result of an elliptic integral inversion.
Keywords Kirchhoff-Poisson equation, Euler-Poisson equation, N. Kovalevski equation, polynomial solutions, Barnett-London effect
UDC 531.38
MSC 70E05, 70E17, 70E40
DOI 10.20537/vm190107
Received 23 February 2019
Language Russian
Citation Zyza A.V. On generalized N. Kovalevski equations in two problems of rigid body dynamics, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2019, vol. 29, issue 1, pp. 73-83.
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