Closed-form solution of pure proportional navigation

The closed-form solution of the equations of motion of an ideal missile pursuing a nonmaneuvering target according to the pure proportional navigation law is obtained as a function of the polar coordinates for all real navigation constants N⩾2. The solution is given in the form of a uniformly convergent infinite product which reduces to a product of a finite number of factors if the navigation constant is a rational number. The solution is discussed, and necessary and sufficient conditions are stated for vanishing, bounded, and unbounded missile acceleration in the final phase of pursuit