COMPUTER SIMULATION OF PARTICLE VELOCITY IN A CYCLONE

The article sets the goal of determining and calculating the speed of accelerated movement of particles in the gas-dust flow of an air cyclone, depending on the size of the cyclone, the physical properties of the particle and the gas-dust flow. A method for constructing a computer model of the motion of a particle in a roaring gas-dust flow of a cyclone is presented. The sequence of formalization of the computer model of the process of sedimentation of particles of a gas-dust flow of a cyclone unit is based on the theoretical foundations of aerodynamics and touches on the most significant aspects of the development of a cyclone. Attention paid to the analysis of the dynamics of particle motion in a centrifugal field, accelerated motion and a realistic estimate of the particle velocity. The mutual influences of five forces are considered. This is the centrifugal force, the force of resistance of the gas-dust flow, the forces of gravity, the Archimedean force and the force of inertia, acting on the accelerating motion of the particle in the flow. On the basis of the block principle, a general computer model of the cycloning process is built, which makes it possible to calculate the uneven velocity of a particle in a gas-dust flow. Analytical methods for evaluating the acceleration parameters and the main methods of numerical analysis of the dynamics of particle motion, shows that the main advantage of up to 0.8 seconds is the accelerated motion of a particle in a gas-dust flow under the given conditions. During this time, most of the particles reach the cyclone wall. This shows that the determination of the accelerating motion of a particle plays an important role in cyclones.

An Alternative Theory on the Spacetime of Non-inertial Reference Frame

In present paper, we have proposed an alternative theory on the spacetime of non-inertial reference frame (NRF) which bases on the requirement of general completeness (RGC) and the principle of equality of all reference frames (PERF). The RGC is that the physical equations used to describe the dynamics of matter and/or fields should include the descriptions that not only the matter and/or fields are at rest, but also they move relative to this reference frame, and the structure of the spacetime of reference frame has been considered. The PERF is that any reference frame can be used to describe the motion of matter and/or fields. The spacetime of NRF is inhomogeneous and deformed caused by the accelerating motion of the reference frame. The inertial force is the manifestation of deformed spacetime. The Riemann curvature tensor of the spacetime of NRF equals zero, but the Riemann-Christoffel symbol never vanishs no matter what coordinate system is selected in the NRF. The physical equations satisfied the RGC remain covariance under the coordinate transformation between the reference frames. Mach’s principle is incorrect. The problem of spacetime of NRF can be solved without considering gravitation.

VIRTUAL MASS OF REGULAR POLYGON AT ANGLE OF ATTACK

In case of the accelerating motion like a sinusoidal motion, the virtual mass effect should be taken into account in equation of motion. Generally speaking we should find the appropriate mapping functions while they are restricted in some functions. To the author's knowledge, the virtual mass of the regular polygon is not shown by the exact solution, while the regular polygon is used as a sectional shape of the structure like a building, a membrance of a structure and so on. It is shown that the virtual mass of an regular polygon has been calculated by using the exact conformal mapping, in which the angle of attack is taken into account. Results show that it is not dependent from the angle of attack except the flat plat (n=2). It means, although the body shape is not a point symmetry, there is no dependence of angle of attack on virtual mass except the flat plate.

On the Stability of Rigid Multibody Systems With Applications to Robotic Grasping and Locomotion

This paper shows that the equilibria of a wide class of multibody systems with quasi-rigid, frictional, or frictionless supports correspond to local minima of their potential energy; hence they are stable against small perturbations of external forces. This is a generalization of a theorem by Howard and Kumar on the stability of a single rigid body held by a gripper. It is also demonstrated that ambiguous equilibria (those, which coexist with the possibility of accelerating motion) may be stable. These results help finding safe grasps on nonrigid objects and assessing the stability of quasi-static robots moving over complex terrains.