Equivalence of the Minimum Norm and Gradient Projection Constrained Optimization Techniques

small that the exact solution, Eq. (27), has only one root at Z = 1. Consequently, the angle of attack variation is the same as that of a critically damped dynamical system as indicated in Fig. 2. The change in reference level(Y = 0) is given for several values of kv For Z > 6 the angle of attack essentially remains zero for the case shown in Fig. 2, and the exact solution given by Eq. (27) for a = — 1 has no oscillations for Z > 1. It is now evident that for a > 10 Alien's approximate solution, as given by Eq. (12), provides an excellent approximation to his differential equation for the straight line descent of a large drag ballistic missile, Eq. (2). It is necessary to introduce the exact solution, Eq. (7), only when a 10.