Applied Mathematics Stabilization of Vertically Modulated Pendulum with Parametric Periodic Forces
With the application of Kapitza method of averaging for arbitrary periodic force, a vertically modulated pendulum, with periodic linear forces is stabilized by minimizing its potential energy function. These periodic linear forces are selected in range [-1, 1], further the corresponding stability conditions are compared with that in case of harmonic modulation. Later, a parametric control is defined on some periodic piecewise linear forces and the nontrivial position is stabilized under different conditions by just adjusting the parameter.
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