Nadezhda Erdakova

In this paper we investigate the dynamics of a body with a flat base (cylinder) sliding on a horizontal rough plane. For analysis we use two approaches. In one of the approaches using a friction machine we determine the dependence of friction force on the velocity of motion of cylinders. In the other approach using a high-speed camera for video filming and the method of presentation of trajectories on a phase plane for analysis of results, we investigate the qualitative and quantitative behavior of the motion of cylinders on a horizontal plane. We compare the results obtained with theoretical and experimental results found earlier. In addition, we give a systematic review of the well-known experimental and theoretical results in this area.

In this paper we investigate the dynamics of a body with a flat base sliding on a inclined plane under the assumption of linear pressure distribution of the body on the plane as the simplest dynamically consistent friction model. Computer-aided analysis of the system’s dynamics on the inclined plane using phase portraits has allowed us to reveal dynamical effects that have not been found earlier.

In this paper we investigate the dynamics of a body with a flat base sliding on a horizontal plane under the assumption of linear pressure distribution of the body on the plane as the simplest dynamically consistent friction model.

For analysis we use the descriptive function method similar to the methods used in the problems of Hamiltonian dynamics with one degree of freedom and allowing a qualitative analysis of the system to be made without explicit integration of equations of motion. In addition, we give a systematic review of the well-known experimental and theoretical results in this area.

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.

The problem of a uniform straight cylinder (disc) sliding on a horizontal plane under the action of dry friction forces is considered. The contact patch between the cylinder and the plane coincides with the base of the cylinder. We consider axisymmetric discs, i.e. we assume that the base of the cylinder is symmetric with respect to the axis lying in the plane of the base. The focus is on the qualitative properties of the dynamics of discs whose circular base, triangular base and three points are in contact with a rough plane.

In this paper, the system of two vortices in an annular region is shown to be integrable in the sense of Liouville. A few methods for analysis of the dynamics of integrable systems are discussed and these methods are then applied to the study of possible motions of two vortices of equal in magnitude intensities. Using the previously established fact of the existence of relative choreographies, the absolute motions of the vortices are classified in respect to the corresponding regions in the phase portrait of the reduced system.

This study is the continuation of the computer experiment [1] with particles of gas in a one-dimensional tube, described earlier. In this paper we give investigation results for the statistical properties of a relativistic gas in a one-dimensional tube. It is shown that this system reaches the state of thermodynamical equilibrium whose distribution function is determined by the relativistic energy of particles. The system of particles in a one-dimensional tube is described by analogy with the billiards in a polygon.

With the help of mathematical modeling, we study the behavior of a gas ($\sim10^6$ particles) in a one-dimensional tube. For this dynamical system, we consider the following cases:
— collisionless gas (with and without gravity) in a tube with both ends closed, the particles of the gas bounce elastically between the ends,
— collisionless gas in a tube with its left end vibrating harmonically in a prescribed manner,
— collisionless gas in a tube with a moving piston, the piston’s mass is comparable to the mass of a particle.
The emphasis is on the analysis of the asymptotic ($t→∞$)) behavior of the system and specifically on the transition to the state of statistical or thermal equilibrium. This analysis allows preliminary conclusions on the nature of relaxation processes.
At the end of the paper the numerical and theoretical results obtained are discussed. It should be noted that not all the results fit well the generally accepted theories and conjectures from the standard texts and modern works on the subject.