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