Source: http://nd.ics.org.ru/archive_nd/tom-8-4/
Timestamp: 2019-04-25 02:02:00+00:00

Document:
The Contensou–Zhuravlev model [1, 2] is extended to include the case of planar elliptic contact of a convex body with a horizontal plane. The Padé approximations of expressions for determining the friction force and friction torque are constructed. The resulting model is applied to the numerical investigation of the dynamics of a homogeneous ellipsoid of revolution on a horizontal plane.
Kuznetsov S. P., Jalnine A. Y., Sataev I. R., Sedova Y. V.
We perform a numerical study of the motion of the rattleback, a rigid body with a convex surface on a rough horizontal plane in dependence on the parameters, applying the methods used previously for the treatment of dissipative dynamical systems, and adapted for the nonholonomic model. Charts of dynamical regimes are presented on the parameter plane of the total mechanical energy and the angle between the geometric and dynamic principal axes of the rigid body. Presence of characteristic structures in the parameter space, previously observed only for dissipative systems, is demonstrated. A method of calculating for the full spectrum of Lyapunov exponents is developed and implemented. It is shown that analysis of the Lyapunov exponents of chaotic regimes of the nonholonomic model reveals two classes, one of which is typical for relatively high energies, and the second for the relatively small energies. For the model reduced to a three-dimensional map, the first one corresponds to a strange attractor with one positive and two negative Lyapunov exponents, and the second to the chaotic dynamics of the quasiconservative type, with close in magnitude positive and negative Lyapunov exponents, and the rest one about zero. The transition to chaos through a sequence of period-doubling bifurcations is illustrated, and the observed scaling corresponds to that intrinsic to the dissipative systems. A study of strange attractors is provided, in particularly, phase portraits are presented as well as the Lyapunov exponents, the Fourier spectra, the results of calculating the fractal dimensions.
Ivanov A. P., Sakharov A. V.
We consider a rigid body which moves upon a rough plane by means of displacements of internal masses. To make turns, we change the angular momentum of the rotor. This leads to asymmetry in normal stresses and appearance of vertical momentum of friction forces.
Ivanov A. P., Erdakova N. N.
The problem of dynamics of heavy uniform ball moving on the fixed rough plane under its own inertia and forces of dry friction is considered. Assuming that friction coefficient is variable, the switching curve for change the value of friction coefficient is constructed. Using this curve to change the value of friction coefficient we have shown that the bundle of equal balls starting from one interval with equal linear and angular velocities should gather at one point.
Borisov A. V., Mamaev I. S., Treschev D. V.
In this paper we investigate various kinematic properties of rolling of one rigid body on another both for the classical model of rolling without slipping (the velocities of bodies at the point of contact coincide) and for the model of rubber-rolling (with the additional condition that the spinning of the bodies relative to each other be excluded). Furthermore, in the case where both bodies are bounded by spherical surfaces and one of them is fixed, the equations of motion for a moving ball are represented in the form of the Chaplygin system. When the center of mass of the moving ball coincides with its geometric center, the equations of motion are represented in conformally Hamiltonian form, and in the case where the radii of the moving and fixed spheres coincides, they are written in Hamiltonian form.
Ramodanov S. M., Tenenev V. A., Treschev D. V.
We study the system of a 2D rigid body moving in an unbounded volume of incompressible, vortex-free perfect fluid which is at rest at infinity. The body is equipped with a gyrostat and a so-called Flettner rotor. Due to the latter the body is subject to a lifting force (Magnus effect). The rotational velocities of the gyrostat and the rotor are assumed to be known functions of time (control inputs). The equations of motion are represented in the form of the Kirchhoff equations. In the case of piecewise continuous controls, the integrals of motion are indicated. Using these integrals we obtain a (reduced) system of first-order differential equations on the configuration space. An optimal control problem for several types of the inputs is then solved using genetic algorithms.
Vetchanin E. V., Mamaev I. S., Tenenev V. A.
An investigation of the characteristics of motion of a rigid body with variable internal mass distribution in a viscous fluid is carried out on the basis of a joint numerical solution of the Navier–Stokes equations and equations of motion. A non-stationary three-dimensional solution to the problem is found. The motion of a sphere and a drop-shaped body in a viscous fluid, which is caused by the motion of internal material points, in a gravitational field is explored. The possibility of motion of a body in an arbitrary given direction is shown.
A critical review of such notions as holonomic and non-holonomic, unilateral and binary constraints is given. The correctness of these models is considered.

References: V.

 V.

 V.

 V. 
 V.

 V.