A mathematical model of pointing an air-to-air missile at an air target of a helicopter class in a stationary mode of its flight

The expansion of the functions and applications of helicopters of various purposes determines the demand for and relevance of the development of new methods and means of their destruction. One promising way to combat helicopter-class aerial targets is to use air-to-air guided missiles. Guided missiles are guided to aerial targets due to implementation of appropriate guidance algorithms in missile computer. Analysis of existing algorithms of guided aircraft missiles guidance to aerial targets showed their insufficient efficiency when guided to a helicopter with different nature of its flight. Therefore, there is an objective need to develop new algorithms that take into account the peculiarities of helicopter flight and ensure optimal control of missile flight when it is directed to the helicopter. As an approach for obtaining optimal algorithms of missile control when pointing on a helicopter, it is proposed to use a mathematical apparatus of statistical theory of optimal control in the space of states. According to this approach, the synthesis of algorithms is based on a mathematical model of mutual movement of a missile and a helicopter during guidance. The existing models do not take into account the peculiarities of dynamics of change of the main parameters of helicopter movement at different nature of its flight. In this connection, the purpose of this article is to develop a mathematical model of mutual movement of the guided missile and the air target of the "helicopter" class. For certainty in this work one of helicopter flight modes - stationary - is considered. The obtained model will be the basis for further development of optimal algorithms of guided missile guidance when guided on a helicopter.