What is it about?
Upon a new mathematical definition (perpetual points) some new definitions have been defined in mathematics (perpetual manifolds and augmented perpetual manifolds) and in mechanics (perpetual mechanical systems) which led to the development of an alternative dynamic analysis of non-ideal mechanical systems e.g., with dry friction etc. whereas when their motion is described by this mathematical formalism they have great behavior, unimaginable too, in terms of mechanics.
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Why is it important?
The alternative new dynamic analysis showed for first time that, I. Many different mechanical systems e.g., in size and/or in internal forces etc., can have the same motion. II. In mechanical systems, the existence of rigid body modes with nonzero frequency is shown/designed. For first time the mechanics of a motion have the following important characteristics, 1. The existence and the prescription of particle-wave motions of flexible mechanical systems. 2. The internal forces of a flexible mechanical system can be zero, therefore the internal components can have no degradation. 3. The existence of nonlinear internal forces (zero) in an flexible mechanical system, is possible not to affect the motion. 4. Internally to a flexible mechanical system, might be no energy storage and no energy loss. 5. A flexible mechanical system can behave as a Perpetual Machine of a third Kind. 6. A flexible mechanical system in reversible dynamics, for the total period, cannot behave as a Perpetual Machine of a third kind.
Perspectives
Regarding the dynamics it should be highlighted that the existence of rigid body modes with nonzero frequency leads to a new design philosophy. Regarding the mechanics of these motions, it should be highlighted that for many many years the researchers were looking for the existence of the perpetual machines rather than the conditions that non-ideal machines can behave as perpetual machines.
Prof. Fotios Georgiades/Georgiadis-FHEA
Read the Original
This page is a summary of: Introduction to the Perpetual Mechanics Theory: The Starting Point and Future Directions, January 2024, Springer Science + Business Media,
DOI: 10.1007/978-3-031-50631-4_46.
You can read the full text:
Resources
NODYCON 2023 presentation with QA
Remotely in about 13 minutes video with the attached slides was my presentation at NODYCON 2023. The slides are self-explained and the presentation has been prepared to explain the prerequisites that undergraduate/postgraduate students in Engineering/Physics/Mathematics must have to follow and repeat the presented results (all the required details are given). In due time the video will be freely available by the conference organizers.
Perpetual Mechanics Theory in a Nutshell
On this presentation, fundamental questions relevant to Perpetual Mechanics Theory are addressed, and they are, -What are the perpetual points and the perpetual manifolds? -What are the rigid body motions of an unloaded mechanical system? (Unforced, therefore the Ideal case) -How is the rigid body motion, of an unloaded linear mechanical system (Ideal Case) related with the perpetual manifolds? -What are the Perpetual Mechanical Systems? -What about rigid body motion of externally loaded mechanical systems? Any significance in mechanics? The Non-Ideal Cases -Is it possible different mechanical systems e.g., in size, to have the same motion? -Why Perpetual Mechanics? -Is the Perpetual Mechanics formalism a useful tool for the design of mechanical systems? -Summary leading to the terminology: 'The Perpetual Mechanics Theory' -What is the history about the so far development of it?
The "History"/Scientific Steps of The Perpetual Mechanics Theory's Development so Far
The "History"/Scientific Steps of The Perpetual Mechanics Theory's Development so Far (10 posts in my “Linked in” account-Sept. & Oct. 2023)
Introduction to The Perpetual Mechanics Theory and Future Directions
It is the extended abstract for NODYCON 2023 participation which led to the published chapter. It forms a 1 page article since it is a self-contained document. Therefore there is sufficient information so all the results can be repeated and, by undergraduate students too. Prerequisite of knowledge, 1) the derivation of the 2 equations which describe the motion of the mechanical system and, 2) the numerical integration of these equations of motion. -Hints for 1) in case of Newton's law use then 2 free body diagrams must be derived. Alternatively, Lagrange equation can be used whereas the kinetic and potential energies (second and fourth order) can be easily derived, the damping forces are linear and the external forces are explicitly defined. -Hints for 2) the numerical simulations can be done with ode45 or adams solver or any other.
Contributors
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