Moving object evasion from single detector at given speed

Within the problem of evasion from detection by a single sensor on a plane at a constant speed the problem is considered of planning the optimal route of a moving object in order to minimize the integral level of the useful signal coming to the observer. It is shown that the various mechanisms of detection of a moving object can be reduced to a general mathematical formalization, namely to the study of the detection problem for different types of signal and a small signal/noise ratio. The study of the two-point variational problem with an integral constraint reduces to solving three types of systems of algebraic-integral equations, which include elliptic integrals of Legendre of the first and second kind, and the system type is determined by different initial conditions and values of the integral constraints. For each of the systems described in the paper, a numerical procedure for its solution is implemented.