Analytical solution of missile terminal guidance

A new guidance law, which combines pursuit guid-ance and proportional navigation is proposed. This guidance law depends on two parameters that de-termine the relative importance of pursuit guidance and proportional navigation. Numerical simulations of the nonlinear equations of motion suggest that the parameters of this law can be chosen to reduce the peak value of the missile acceleration. When the engagement ends in a tail chase, and linearization is valid, the linearized equations of motion lead to a confluent hypergeometric equation. This equation is solved in closed form, in the general case where the target performs maneuvers such that its head-ing angle is a polynomial function of time. The ana-lytic solution based on linearization and the numeri-cal simulation of the nonlinear equations show good agreement. Nomenclature a, b = parameters in normalized guidance law Ci = constants of integration / = forcing function k { = coefficients of forcing function m — degree of polynominal n = velocity ratio R = relative distance r = normalized relative distance t — flight time VM — missile velocity VT — target velocity z = modified relative distanc