Abstract
The optimal control of the deceleration of a particle moving along a straight line after an impact against an isolated surface is considered. The force applied to the particle by the surface is treated as the control variable. The deceleration distance is minimized subject to a constraint on the Head Injury Criterion functional. This functional is an integral criterion that is utilized in engineering biomechanics to evaluate the expected severity of impact-induced head injury of a human being. The solution obtained provides characteristics of the limiting capabilities for the prevention of head injuries by means of an impact isolator, such as a coating of the surface against which the impacts occur. The head injuries can be due to impact occurrences, including traffic crashes, falling, and contacts with ballistic objects.