This article is cited in 1 paper

Original papers

On the motion of a heavy rigid body in two special cases of S.V.Kovalevskaya’s solution

G. V. Gorr^a, E. K. Shchetinina<sup>b

a</sup> Institute of Applied Mathematics and Mechanics, ul. R. Luxemburg 74, Donetsk, 283114, Ukraine
^b Kyiv National University of Trade and Economics, ul. Kioto 19, Kiev, 02156, Ukraine

Abstract: Two particular cases of the Kovalevskaya solution are studied. A modified Poinsot method is applied for the kinematic interpretation of the body motion. According to this method, the body motion is represented by rolling without sliding of the mobile hodograph of the vector collinear to the angular velocity vector along the stationary hodograph of this vector. Two variants are considered: the first variant is characterized by a plane hodograph of the auxiliary vector; the second variant corresponds to the case where the hodograph of this vector is located on the inertia ellipsoid of the body.

Keywords: Kovalevskaya’s solution, Poinsot’s method.

UDC: 531.381; 531.391

MSC: 70E17, 70E40

Received: 12.09.2017
Accepted: 12.01.2018

DOI: 10.20537/nd1801010

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