The Closed Form Solution of True Proportional Navigation

The closed form solution of the equations of motion of an ideal missile pursuing a non-maneuvering target according to the true proportional navigation (TPN) law is obtained. In this case, commanded accelerations are applied in a direction normal to the interceptor-target line of sight. A linearized analysis is applied to study the TPN and a circle is found where capture can be demonstrated. A major point of this study is that the analysis of the closed form solution of TPN enables one to demonstrate the basic differences existing between the two most utilized forms of proportioned navigation, namely that pure proportional navigation has a much different capture envelope than the circle described for TPN. (Author)