Abstract

Perpetual points have been defined recently and they have been associated with hidden attractors. The significance of these points for the dynamics of a system is ongoing research. Herein, a theorem is presented, describing the nature of the perpetual points in linear natural conservative mechanical systems and as it is shown they are defining the rigid body motions and vice versa. Subsequently, the perpetual points of two conservative nonlinear mechanical systems are determined. The first one is a two degrees of freedom nonlinear natural mechanical system and, as it is shown there are two sets of perpetual points which are associated with the rig-id body motions. The other system is a non-natural conservative system, a flexible spinning shaft with non-constant rotating speed and, as it is shown, there are also three sets of perpetual points, and all of them are associated with the rigid body motions. In all examined nonlinear systems, the same observation made, that the perpetual points are associated with the rigid body motions, but formal proofs with the associated conditions as future work should be considered to generalise this observation. This work is essential to understand the nature of perpetual points in mechanical systems and opens new horizons for new operational modes and new design processes, targeting the ultimate operational modes of many mechanical systems which are the rigid body motions without having any vibrations.