Рассмотрен один из возможных подходов к математическому моделированию загрузки робототехнического комплекса (РТК) тяжелого класса на гусеничном шасси с независимой торсионной подвеской в транспортный самолет. Данный подход представляет собой часть обоснованной оценки авиатранспортабельности специальных РТК. Он базируется на построении и решении системы линейных уравнений, в результате чего определяются параметры, по которым оценивается факт «вписывания» конструкции образца РТК в размеры грузовой кабины самолета. Актуальность статьи обусловливается, во-первых, потребностью в создании специальных РТК тяжелого класса для применения при тушении пожаров на особо опасных объектах, во-вторых, значительным вкладом оценки возможностей по загрузке в самолеты РТК в априорную аналитическую оценку авиатранспортабельности специальных РТК как до создания опытных образцов, так и в ходе оперативной подготовки к перебазированию в районы чрезвычайных ситуаций и, в третьих, определенной сложностью графоаналитического моделирования рассматриваемой загрузки.
The threat of man-made danger with such sources as accidents at radiation, chemical and explosive objects exists at present time. That’s why it is advisable to create heavy-class fire robotic complexes on a tracked chassis, as the most effective means of extinguishing fires in these conditions. The consequences of emergencies depend on a quick and timely response. Therefore, when creating the new promising fire equipment, one of the most important issues to be addressed is to ensure its air transportability. At the stage of development of advanced heavy-class fire-fighting robotic systems on a tracked chassis with the planned possibility of their air transportability, it is very important to perform an a priori assessment of this property before creating a prototype. Modeling of loading involves solving a variety of problems, the main and most complex of which is the calculation of the spatial position of the structure of a particular robotic complex model with a tracked chassis relative to the internal contours of the cargo cabin of the aircraft. There are several types of structures for springing support rollers of tracked chassis. This article discusses tracked chassis with independent torsion bar suspension widely used in modern military equipment. It is advisable to focus the development of heavy-class fire robotics on the use of torsion bar suspension. The calculation of parameters that form the basis of mathematical modeling consists in solving a system of nonlinear equations (including algebraic and trigonometric operations). One of the equations describes the condition of the equilibrium of forces, the second - the equilibrium of moments, the rest (according to the number of support rollers minus one) describe the conditions for the location of the torsion axes on a given construction axis. The proposed calculation method provides for the transformation of this system into a system of linear algebraic equations which ensure an approximate solution, and the organization of an iterative process that ensures the convergence of a sequence of approximate solutions to the solution of the original system of nonlinear equations. The approach presented in the article can be used as the basis for modeling the loading of a special robotic complex on a tracked chassis with an independent torsion suspension into the cargo cabin of a transport aircraft. In turn, this modeling allows us to perform the reasonable a priori assessment of the air transportability of the robotic complex, carried out both at the stage of layout of the sample during its creation and during operation.
Existence of solutions of a two-dimensional boundary value problem for a system of nonlinear equations arising in growing cell populations
