Applied Mathematics Stabilization of Vertically Modulated Pendulum with Parametric Periodic Forces

Applied Mathematics Stabilization of Vertically Modulated Pendulum with Parametric Periodic Forces

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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 THE RISKS ON THE RUSSIAN FINANCIAL MARKET IN THE CONDITIONS OF GLOBALIZATION [-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 Exercise training does not improve myocardial diastolic tissue velocities in Type 2 diabetes by just adjusting the parameter.