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ENGINEERING METHOD FOR MODELING THE OUTER BALLISTICS OF ROTATIONAL AND PROGRESSIVE MOVEMENT DUMBBELLS

The work is devoted to the method of delivering a fire extinguishing agent into a distant fire zone. In a known method, a substance (for example, a fire extinguishing powder) is placed in a solid shell - a cylindrical container. After delivery to the location of the fire, the container should collapse and free up the substance that will be assisted on fire extinguishing. A pneumatic gun is used to deliver a cylindrical container. In the process of delivery, the cylinder should rotate around its axis to ensure the stability of the movement. At the same time, during the "shot", the difficulty of regulating the distribution of compressed air flows in the gun dulk to achieve the required speed of rotation of the cylinder is arisen. 
In a new delivery method, it is proposed to use a container consisting of two spherical containers connected by a rod (like dumbbells). Traditional motion modeling Dumbbells is based on the preparation and solution of the system of differential equations of Lagrange of the second kind. To do this, choose the functions of generalized coordinates and use Lagrangian to describe the rotational and progressive movement of dumbbells in the earth's field. This allows you to obtain approximate functional dependences, as well as dependencies of derivatives for each of the functions of generalized coordinates. As a result, you can depict charts of phase trajectories of the generalized coordinates. The dependence on time for the functions of generalized coordinates allow you to simulate the outer ballistics dumbbells - i.e. Create a computer animation of its rotational and progressive movement. 
In contrast to the traditional approach in this paper, an engineering method of geometric modeling of the external ballistics of the movement of dumbbells is proposed. Those. The method of modeling the rotational and progressive movement dumbbells, which is based on geometric representations. We assume that the auxiliary circle is rigidly fixed on the dumbbells, the center of which coincides with the center of mass dumbbells. Let the circle "quoted" along the ballistic trajectory of the Mass Dumbbell Center. Then the trajectories of the point mass of cargo dumbbells will give an approximate view of the rotational and progressive movement of dumbbells into spacious within the vertical plane. 
 