Stability of Potential Systems to General Positional Perturbations

What is it about?

This paper shows that civil, aerospace, and mechanical, potential systems that have multiple frequencies of vibrations are unstable and can be destabilized by infinitesimal perturbatory forces. The structure of the uncountably infinite number of matrices that describe these perturbatory forces are explicitly provided. When two frequencies of vibration in a potential system are 'close', but nor (mathematically) identical, as often happens in real-life systems, then an uncountably infinite number of matrices that correspondingly describe 'small' perturbatory forces will cause the system to become unstable. The meanings of the words 'close' and 'small' are precisely defined in the paper.

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