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<p><i>A generalization of the classical Kapitza pendulum — a planar mathematical pendulum on a vibrating base — is considered in the case where an additional horizontal force acts on the pendulum. It is shown that for a sufficiently high frequency of base vibrations there exists a one-parameter family of solutions to the system along which the pendulum does not become horizontal and is left strictly in the upper half-plane. The proof employs a topological-analytical approach to infinite-time averaging. Bibliography:</i> 9 <i>titles. Illustrations:</i> 2 <i>figures</i>.</p>

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THE KAPITZA-WHITNEY PENDULUM: AVERAGING OVER AN INFINITE INTERVAL IN THE CASE OF A NON-PERIODIC RIGHT-HAND SIDE

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Ivan Yu. Polekhin

摘要

A generalization of the classical Kapitza pendulum — a planar mathematical pendulum on a vibrating base — is considered in the case where an additional horizontal force acts on the pendulum. It is shown that for a sufficiently high frequency of base vibrations there exists a one-parameter family of solutions to the system along which the pendulum does not become horizontal and is left strictly in the upper half-plane. The proof employs a topological-analytical approach to infinite-time averaging. Bibliography: 9 titles. Illustrations: 2 figures.