The motion of a pendulum system under the action of vibration, the frequency of which substantially exceeds the frequencies of eigen vibrations of the system was studied. Instead of two approximations in the parameter, it required only one averaging over the period of the Hamiltonian function in the proposed modification. The motion of the system is determined from the Lagrangian equations with the Lagrangian function. From the Lagrangian function, it is possible to construct the Hamiltonian function. The problem on the steady periodic motion is reduced to determining the point of the minimum of the effective potential energy.
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