In linear, and some nonlinear unforced mechanical systems they are associated with rigid body motions [Georgiades 2020 IUTAM, and Georgiades 2021 Proc. IMechE] and they are infinite points (forming manifolds). Therefore under conditions they can form solutions of differential equations that describe rigid body indefinite motions.

The unforced, linear and nonlinear, mechanical systems with infinite perpetual points associated with rigid body motion are called perpetual mechanical systems, and this definition applies in linear and nonlinear mechanical systems [Georgiades 2021 ASME JCND]. Therefore these systems are possible to move indefinitely in rigid body motion, and this justifies the terminology. The perpetual mechanical systems configuration can be in two possible ways, without any structural element attached to the ground or with structural elements as boundaries of them attached to the ground. Also they can have any, greater than 2, number of degrees of freedom.

The augmented perpetual manifolds are defined as the infinite sets of points of anexternally forced perpetual mechanical system that arise when we set all accelerations equal but not necessarily zero. Upon the initial conditions the equal accelerations define exact rigid body motions and these solutions are called exact augmented perpetual manifolds[Georgiades 2021 ASME JCND]. In case that the accelerations are zero then they coincide with the perpetual manifolds, and this justifies the terminology (augmented).

The exact augmented perpetual manifolds are defining rigid body motions of externally forced perpetual mechanical systems without any oscillations which is the ultimate motion in many mechanical structures e.g. car, train, bicycle, airplane, etc.Therefore the N-degrees of freedom mechanical system, in the exact augmented perpetual manifolds, is moving like a particle. Moreover, these motions of the mechanical systems can have infinite functional forms [Georgiades 2021 SSCM] e.g. particle linear,  particle-curvilinear form, particle-standing wave, particle-longitudinal wave etc.

The dynamics of perpetual mechanical systems can deal only with the dynamics of the mechanical systems. The dynamics of mechanical systems in the exact augmented perpetual manifolds, with the view of mechanics, is associated with certain characteristics:

The linear and the nonlinear perpetual mechanical systems for the same external forcing they have the same motion [Georgiades 2021 IJNM]. Therefore to study the dynamics of the perpetual mechanical systems in the exact augmented perpetual manifolds there is no need of cumbersome nonlinear modelling.

The sum of the internal forces of the perpetual mechanical system, when the dynamics is described by an exact perpetual manifold, is equal to zero [Georgiades 2021, NODYCON].

The natural perpetual dissipative mechanical systems, when their motion is described by the exact augmented perpetual manifolds, under certain conditions, can have eliminated all the individual internal forces, no internal dissipation, the kinetic energy changes is equal with the external forces work done, and these systems might behave as perpetual machines of third kind [Georgiades 2022, Nonlinear Dynamics]. All these conclusions are rather significant in terms of mechanics as a consequence of the dynamics of the perpetual mechanical systems in the exact augmented perpetual manifolds.

Therefore the examination of the dynamics of the perpetual mechanical systems with their associated internal forces and their energy exchange with the environment is called perpetual mechanics.

1. Georgiades, F., 2021, Augmented Perpetual Manifolds and Perpetual Mechanical Systems-Part I: Definitions, Theorem and Corollary for Triggering Perpetual Manifolds, Application in Reduced Order Modeling and Particle-Wave Motion of Flexible Mechanical Systems, Journal of Computational and Nonlinear Dynamics, Jul 2021, 16(7): 071005 (19 pages).

Prof. Ivana Atanasovska, Mathematical Institute of Serbian Academy of Sciences and Arts –MI SANU(Serbia)

Assist. Prof. AndjelkaHedrih, Mathematical Institute of Serbian Academy of Science and Arts-MI SANU (Serbia)

Organised the Special Issue “Nonlinear Dynamics of Mechanical Systems” dedicated to 75th birthday and 52 years scientific contribution of Prof. Katica R. (Stevanovic) Hedrih in Journal of Mechanical Science of IMechE Part C, and the Director of CPM, while working for the establishment of CPM, with Chennai Institute of Technology affiliation published the editorial preface and the tribute to Prof. Hedrih.