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We consider the problem of the motion of a heavy dynamically symmetric rigid body bounded by a surface of rotation on a fixed perfectly rough horizontal plane. The integrability of this problem was proved by S.A. Chaplygin []. Chaplygin has found that the equations of motion of given mechanical system have, besides the energy integral, two first integrals, linear in generalized velocities. However, the explicit form of these integrals is known only in the case, when the moving body is a nonhomogeneous dynamically symmetric ball. In the case, when the moving body is a round disk or a hoop, the integrals, linear in the velocities, are expressed using hypergeometric series [],[],[]. In the paper of Kh.M. Mushtari [] the investigation of this problem was continued. For additional restrictions, imposed on the surface of moving body and its mass distribution, Mushtari has found two particular cases, when the motion of the body can be investigated completely. In the first case the moving rigid body is bounded by a surface formed by rotation of an arc of a parabola about the axis, passing through its focus, and in the second case, the moving body is a paraboloid of rotation. For other bodies, bounded by a surface of rotation and moving without sliding on a horizontal plane, the explicit form of additional first integrals is unknown.

In this work we find some new cases when all the integrals of the problem can be expressed explicitly, when the surface of moving body satisfies to a Mushtari condition. The set of surfaces of moving bodies satisfying to this condition is described.

Pulp for making paper is produced in the groundwood (GW) process from logs. In batch-type GW-machines the control of the log loading is a demanding task because of the complicated log group dynamics where also the heterogeneous wood material has a great influence on the batch behaviour. It is essential to achieve better understanding of the regularities occurring in the process in order to improve the loading control and thus the quality and efficiency of pulp production. For this purpose a numerical model of the complete process has been built up and the dynamic system behaviour has been studied by time domain simulation. In this paper the focus is in the description of the log batch behaviour. Three separate approaches have been adopted to model the batch.

This paper focuses on investigating systematically the phenomenon of the bouncing motion when a robotic manipulator slides on a rough surface. From the viewpoint of rigid body dynamics, this phenomenon is related to the dynamical properties of a multi-rigid-body system subject to unilateral constraints with friction. Applying the LCP (Linear Complementary Problem) theory, we can classify the bouncing motion into two cases: one that is due to the action of inertia of system; the other that is due to the singularities of rigid-body model induced by friction forces. As an example of a planar multibody system with single unilateral constraint, the admissible set for a two-link manipulator is studied in detail. Meanwhile, The numerical results show that the paradoxes in rigid body model can occur even if the value of coefficient of friction is very small.

One challenge of todays research on particle systems is the realistic simulation of granular materials consisting of many thousands of particles with peculiar contact interactions. In this study, molecular dynamics (MD, also called discrete element method, DEM) is introduced for the simulation of many-particle systems. A wide class of realistic contact models is presented, involving dissipation, adhesion, plastic deformation, friction, rolling- and torsion resistance.

The effect of the contact properties on a simple compaction test is discussed with the goal to achieve as small as possible packing densities. With contact forces only, packing volume fractions down to 0.42 can be achieved, while somewhat longer ranged adhesion forces allow for volume fractions as low as 0.34.

This work presents the numerical simulation of rolling bodies in three dimensions with multigrid-methods and boundary discretization. The use of different scales during the calculation overcomes known problems, regarding convergence velocity and required time for summations. The final objective is the study of roughness in dry, tangential contact. Discretization up to 300 × 300 points are shown.

Geometrical assumptions and formulation of boundary conditions follow the pioneering work in numerics of contact by []. He developed different algorithms for various simplifications, and most of them are based on maximizing complementary energy. In this case there are proofs for existence and uniqueness of solutions. A serious disadvantage is a relationship of cubic order between number of unknowns and calculation time. This problem makes it impossible to handle fine resolutions, even with fast computers. A set of multigrid methods, introduced by for contact with separating film of liquid [] is used to solve this problem.

Contact areas between rough surfaces can be structured finely, therefore, the method of grid-transformation must be chosen carefully. The common geometry, used in literature, leads to an incorrect mapping of areas, thus existing methods are reformulated with suitable geometry. The problems appeared also in normal contact, were the adapted methods have been applied successfully [].

In contrast to finite elements, the discretization of the boundary method can be restricted to the potential contact area. That way discretizations up to 300 × 300 points are accessible, which is sufficient for study of disturbed surfaces. The influence coefficients, that appear in the boundary approach, can be saved in reduced form under assumption of smooth macro-geometries.

We sketch two different theories for for granular media: a rigid particle theory, where the deformation of grains is neglected, and a quasi-rigid particle theory, where their deformation is taken as infinitesimally small. Both theories are applied to a simple system that can be analytically solved, and results are compared with simulations. In certain situations, self-canceling forces can affect the motion of the particles, in spite of causing no acceleration.

The motion of a simply supported beam struck by a spherical ball is studied. Time scales are identified, which reveal the relative importance of several effects. The resulting motion is calculated with the aid of fundamental solutions. It is shown that the approach leads to results that agree with those obtained by means of a spatial discretization. A further development into a generally applicable method remains a subject for further investigations.

For more general introduction to analytical contact analysis, see [] and [], and for more general introduction to numerical contact analysis, see []. In this paper we present something in-between analytical solutions and advanced numerical solutions; a direct numerical analysis of elastic contact without incrementation and iteration. As a short introduction the main parameters of analytical contact analysis are presented.

Intermittent-motion mechanisms play an important role in modern technology. For instance they are key elements of many automatic machines. Scientific literature records different modelling analyses of this kind of mechanism (e.g. [, ]). Due to the widespread use of such devices, their analysis and design taking into account impact phenomena appears to be significant.

In the great majority of railway networks the electrical power is provided to the locomotives by the pantograph-catenary system. From the mechanical point of view, the single most important feature of this system consists in the quality of the contact between the contact wire(s) of the catenary and the contact strips of the pantograph. Therefore not only the correct modeling of the catenary and of the pantograph must be achieved but also a suitable contact model to describe the interaction between the two systems must be devised. The work proposed here aims at enhancing the understanding of the dynamic behavior of the pantograph and of the interaction phenomena in the pantograph-catenary system. The catenary system is described by a detailed finite element model of the complete subsystem while the pantograph system is described by a detailed multibody model. The dynamics of each one of these models requires the use of different time integration algorithms. In particular the dynamics of the finite element model of the catenary uses a Newmark type of integration algorithm while the multibody model uses a Gear integration algorithm, which is variable order and variable time step. Therefore, an extra difficulty that arises in study of the complete catenary-pantograph interaction concerns the need for the cos-imulation of finite element and multibody models. As the gluing element between the two models is the contact model, it is through the representation of the contact and of the integration schemes applied for the finite and multibody models that the co-simulation is carried on. The work presented here proposes an integrated methodology to represent the contact between the finite element and multibody models based on a continuous contact force model that takes into account the co-simulation requirements of the integration algorithms used for each subsystem model.