Exact augmented perpetual manifolds of periodic motions, a corollary for natural perpetual mechanical systems behaving partially as perpetual machines of third kind

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Perpetual manifolds have been defined recently and in unforced linear natural mechanical systems, they are associated with rigid body motions. The concept has been extended to the exact augmented perpetual manifolds, for externally forced natural mechanical systems in rigid body motion. Under conditions, that a theorem is defining, the natural mechanical systems in rigid body motions can behave as perpetual machines of a third kind, whereas there is no internal energy loss due to damping. In this article, a corollary is stated and proved that the mechanical systems in periodic rigid body motion, therefore also in a reversible process, cannot behave as perpetual machines of a third kind in all time instants. The corollary with an analytical example is verified. Then the analytical findings with the numerical simulations of a mechanical system have been confirmed with excellent agreement. This work is significant in understanding the behavior of mechanical systems as perpetual machines of a third kind. As future work, it can be the identification of external forces types that are leading to perpetual machines of third kind behavior for all the time instants.