Теоретичне обґрунтування для практичної реалізації аналітичного комп’ютерного побудування динамічних рівнянь в псевдокоординатах керованого польоту БПЛА

The article outlines important issues of the theoretical basis for controlling unmanned aerial vehicles (UAVs). The relevance of the topic of the article is based on the great demand for the use of UAVs in various fields. Control methods should be based on appropriate algorithms for solving UAVs flight dynamics problems. The article has developed an algorithm for creating in computer algebra systems the automatic calculation of the dynamics of discrete mechanical systems in an analytical form. This is due to the need to carry out the development of dynamics, structure, systems of UAVs, the structure of mechanical models of which can be significantly modified. Therefore, there is a need for implementation of algorithms, such as a formal description of the mechanical model on the formula level, there will be similar levels and carry out the development of the modeled structure of systems with a spacious flow. The dynamics of discrete models are immediately clearly demonstrated in accordance with the fundamental principle of mechanics – the fundamental variational equation. The alignment of dynamics in coordinated coordinates has been extracted from a vector-matrix view, manual for computer implementation. The principle of the validity of the manifestation of the mechanical state of systems in formal and pseudo (quasi) coordinates is explained. Based on the principle of differentiation of functions of localized coordinates behind pseudo-coordinates, by replacing the formulas for variation of localized coordinates, the normalized speeds of which can be expressed through pseudo-coordinates, dynamic coordinates are derived at pseudo-coordinates. A method for transforming such equations to the Cauchy form is proposed, which allows for the development of numerical methods for integrating such equations. It has been theoretically proven that for UAV models - single or group, the use of pseudocoordinates makes the creation of dynamic equations of motion much simpler compared to the use of traditional generalized coordinates.