Stabilization of Driven Pendulum with Periodic Linear Forces

Using Kapitza method of averaging for arbitrary periodic forces, the pendulum driven by different forms of periodic piecewise linear forces is stabilized. These periodic piecewise linear forces are selected in the range [−1,1] to establish an exact comparison with harmonic forces. In this contest, the rectangular force was found to be the best, but this force is more effective when it has a time-dependent structure. This time-dependent structure is found by defining a parametric control on some other periodic piecewise linear forces