Introduction to the Perpetual Mechanics Theory: The Starting Point and Future Directions

The application of the perpetual points formalism to ideal mechanical systems (unforced), and its expansion to non-ideal mechanical systems, has led to the development of a mathematical framework for the examination of rigid body motions of mechanical systems with essential properties in terms of mechanics. In this chapter, a dynamic analysis with direct attack to the equations of motion of ten examples initially is performed, whereas there is hidden information on the dynamics/mechanics of these systems. This information demonstrated, by presenting an analysis in a more structured way using relevant theorems and corollaries. As a summary for the first time in mechanics, particle-wave motion, motion of mechanical systems with no degradation, no energy loss, and perpetual machines of third-kind behavior are outlined. Moreover, the formalism is used as a tool for the determination of nonlinear normal modes, and for passive control of vibration’s design of mechanical systems. Therefore, the developed formalism can arguably be claimed to form the starting point of the perpetual mechanics theory. Possible, future research directions are presented too.