Gennady Gorr

    ul. R. Luxemburg 74, Donetsk, 283114, DPR, Russia
    Institute of Applied Mathematics and Mechanics


    Gorr G. V.
    This paper is concerned with a special class of precessions of a rigid body having a fixed point in a force field which is a superposition of three homogeneous force fields. It is assumed that the velocity of proper rotation of the body is twice as large as its velocity of precession. The conditions for the existence of the precessions under study are written in the form of a system of algebraic equations for the parameters of the problem. Its solvability is proved for a dynamically symmetric body. It is proved that, if the ellipsoid of inertia of the body is a sphere, then the nutation angle is equal to $\arccos \frac{1}{3}$. The resulting solution of the equations of motion of the body is represented as elliptic Jacobi functions.
    Keywords: three homogeneous force fields, precessions, dynamically symmetric bodies, elliptic functions
    Citation: Gorr G. V.,  On a Class of Precessions of a Rigid Body with a Fixed Point under the Action of Forces of Three Homogeneous Force Fields, Rus. J. Nonlin. Dyn., 2023, Vol. 19, no. 2, pp.  249-264
    Gorr G. V., Tkachenko D., Shchetinina E. K.
    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
    Gorr G. V., Shchetinina E. K.
    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
    Gorr G. V.
    The Bobylev–Steklov solution belongs to one of the most well-known particular solutions of the Euler–Poisson equation of the problem of motion of a heavy rigid body with a fixed point. It is characterized by two linear invariant relations and can be expressed as elliptic functions of time. The interpretation of the motion of the Bobylev–Steklov gyroscope was carried out by P.V. Kharlamov using the Poinsot method. Analysis of the neighborhood of the Bobylev–Steklov solution in the integral manifold of the Euler–Poisson equations was presented by B.S. Bardin for the case where this solution describes pendulum motions. It is therefore of interest to study the general case of the above-mentioned manifold. Using the first Lyapunov method, a new class of asymptotic motions is obtained for a heavy rigid body whose limit motions are described by the Bobylev–Steklov solution.
    Keywords: the first Lyapunov method, Bobylev–Steklov solution
    Citation: Gorr G. V.,  On asymptotic motions of a heavy rigid body in the Bobylev–Steklov case, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 4, pp.  651–661
    Gorr G. V., Maznev A. V.
    The motion of symmetric gyrostat with a variable gyrostatic moment in two tasks of dynamics: in a task about motion of gyrostat under the action of potential and gyroscopic forces and in a task about motion of gyrostat in the magnetic field taking into account the effect of Barnett–London is considered. The decisions of equalizations which contain six arbitrary permanent are indicated.
    Keywords: symmetric gyrostat, equalizations of Kirhgof–Poisson, effect of Barnett–London
    Citation: Gorr G. V., Maznev A. V.,  About motion of symmetric gyrostat with a variable gyrostatic moment in two tasks of dynamics, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 2, pp.  369-376

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