On - off controls in the problem of bending beams

Abstract

In this paper, the Pontryagin’s maximum principle was applied to determine the rule of cross-sectional of a bending beam subjected to self-weight load in the case of the maximum deflection. The research result of the On - Off control showed that there is a two-step beam. For the controlling one, therefore, needs to determine  the position of switch point and the influence of self-weight load to the position of switch point.