Engineering Optimization: Theory and Practice, Fourth Edition

1.5 Classification of Optimization Problems 17

Figure 1.9 Control points in the path of the rocket.

SOLUTION Let points (or control points) on the path at which the thrusts of the
rocket are changed be numbered as 1, 2 , 3 ,... ,13 (Fig. 1.9). Denotingxias the thrust,
vithe velocity,aithe acceleration, andmithe mass of the rocket at pointi,Newton’s
second law of motion can be applied as

net force on the rocket=mass×acceleration

This can be written as

thrust−gravitational force−air resistance=mass×acceleration