# Elena Shchetinina

ul. Kioto 19, Kiev, 02156, Ukraine
Kyiv National University of Trade and Economics

## Publications:

 Gorr G. V., Tkachenko D., Shchetinina E. K. Research on the Motion of a Body in a Potential Force Field in the Case of Three Invariant Relations 2019, Vol. 15, no. 3, pp.  327-342 Abstract The problem of the motion of a rigid body with a fixed point in a potential force field is considered. A new case of three nonlinear invariant relations of the equations of motion is presented. The properties of Euler angles, Rodrigues – Hamilton parameters, and angular velocity hodographs in the Poinsot method are investigated using an integrated approach in the interpretation of body motion. Keywords: potential force field, Euler angles, Rodrigues – Hamilton parameters, Poinsot method Citation: Gorr G. V., Tkachenko D., Shchetinina E. K.,  Research on the Motion of a Body in a Potential Force Field in the Case of Three Invariant Relations, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 3, pp.  327-342 DOI:10.20537/nd190310
 Gorr G. V., Shchetinina E. K. On the motion of a heavy rigid body in two special cases of S.V.Kovalevskaya’s solution 2018, Vol. 14, no. 1, pp.  123-138 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 Citation: Gorr G. V., Shchetinina E. K.,  On the motion of a heavy rigid body in two special cases of S.V.Kovalevskaya’s solution, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 1, pp.  123-138 DOI:10.20537/nd1801010