Zapolskyi L. Geometrical technologies of impulse-inertial formation of kernel structures

The work is devoted to solving a scientifically applied problem - development of geometric technologies of impulse-inertial transformation of bar structures when simulating the construction of objects in zero gravity using pyro-cartridges as movers. Only geometric models of the disclosure process are considered in the work, and their implementation in real products needs the help of process engineers. A geometric model of a pulsed inertial technology for the disclosure of rod structures in zero gravity, as well as a concept for visualizing the mutual positions of structural parts by means of computer animation, have been developed. A method for stopping the process of opening a chain of rods in a previously calculated open state by fixing the mechanism of cylinder joints is proposed. Estimates of the ranges of speeds, accelerations and acting forces on the nodal elements of the rod structures are provided. As an example, a method for the formation of mesh structures in zero gravity based on the coordinated movements of two-link rod mechanical systems, as well as the diagrams of geometric models for the formation of rod structures, such as captures outside the spacecraft, are given. A method for the formation of rod structures in space is proposed by analogy with a four-link pendulum with a moving reference point. Computer experiments were carried out to study the stability of the motion of a rigid body in zero gravity by computer implementation of the Poinsot model. For each of the examples, the arrangement of the elements of four-link bar mechanisms in the process of disclosure was calculated and constructed; phase trajectories of the functions of generalized coordinates, which allow you to determine the range of changes in the values of angles and speeds of disclosure; graphs of the time variation of the angles as functions of the generalized coordinates, as well as the first and second derivatives of these functions; graphs of acceleration and force characteristics of the change in the values of angles as functions of generalized coordinates. The results of theoretical studies were introduced during the development of software for modeling and visualization of the disclosure of rod structures in zero gravity. The development of theoretical bases for modeling geometric objects based on the use of applied geometry requires solving a number of theoretical and practical issues that make the relevance of the research. First of all, it concerns the approach to initiate the movement of elements of a multi-link structure in the process of opening. Geometric models are designed for sequencing illustration of configurations as space objects are transformed into space. The transformation of ultralight frames connected to a chain by means of cylindrical joints in which the whole mass of the structure is concentrated is considered in the work. The opening of the four-link framed structure, as an example, is considered weightless as an analogue of the «oscillation» of the four-link pendulum. It is advisable to investigate the dynamics of the process of opening a structure in the form of a four-link framed system on the basis of the Lagrangian variational principle. The question arises about the adaptation to the weightlessness of the motion of the four-link pendulum as the basis of the geometric model of the orbital object opening. The answer to this question is found in papers on the use of Lagrange equations of the second kind for mechanical systems in weightlessness. It is considered formally that the calculations of transformation of mechanical framed structures in weightlessness can be approximated using only the concepts of kinetic energies. Geometric modeling is manifested in computer animated films created, which show the mutual movement of the links of the framed structures in the process of opening. This allows you to determine the geometric configuration of the location of the links at a certain point in time of opening, depending on the parameters of the framed structure. Keywords: rod structure, generalized coordinates, impulse-inertial disclosure, functions of generalized coordinates, phase trajectory, Poinsot geometric picture, visualization of the disclosure of the structure.