scholarly journals Comments on “The Principle of Least Action for Reversible Thermodynamic Processes and Cycles”, Entropy 2018, 20, 542

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 980 ◽  
Author(s):  
Edward Bormashenko
Keyword(s):  
Variational Problem ◽  
Heat Generation ◽  
Carnot Cycle ◽  
Transversality Conditions ◽  
Rectangular Shape ◽  
Least Action ◽  
Principle Of Least Action ◽  
Thermodynamic Processes

The goal of this comment note is to express my concerns about the recent paper by Tian Zhao et al. (Entropy 2018, 20, 542). It is foreseen that this comment will stimulate a fruitful discussion of the issues involved. The principle of the least thermodynamic action is applicable for the analysis of the Carnot cycle using the entropy (not heat) generation extrema theorem. The transversality conditions of the variational problem provide the rectangular shape of the ST diagram for the Carnot cycle.

scholarly journals The Principle of Least Action for Reversible Thermodynamic Processes and Cycles

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 542 ◽  
Author(s):  
Tian Zhao ◽  
Yu-Chao Hua ◽  
Zeng-Yuan Guo
Keyword(s):  
Heat Release ◽  
Optimization Problems ◽  
Optimal Path ◽  
Classical Mechanics ◽  
Carnot Cycle ◽  
Heat Absorption ◽  
Least Action ◽  
Principle Of Least Action ◽  
Thermodynamic Processes ◽  
Release Processes

The principle of least action, which is usually applied to natural phenomena, can also be used in optimization problems with manual intervention. Following a brief introduction to the brachistochrone problem in classical mechanics, the principle of least action was applied to the optimization of reversible thermodynamic processes and cycles in this study. Analyses indicated that the entropy variation per unit of heat exchanged is the mode of action for reversible heat absorption or heat release processes. Minimizing this action led to the optimization of heat absorption or heat release processes, and the corresponding optimal path was the first or second half of a Carnot cycle. Finally, the action of an entire reversible thermodynamic cycle was determined as the sum of the actions of the heat absorption and release processes. Minimizing this action led to a Carnot cycle. This implies that the Carnot cycle can also be derived using the principle of least action derived from the entropy concept.

scholarly journals Reply to the Comments on: Tian Zhao et al. The Principle of Least Action for Reversible Thermodynamic Processes and Cycles. Entropy 2018, 20, 542

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 986
Author(s):  
Zeng-Yuan Guo ◽  
Tian Zhao ◽  
Yu-Chao Hua
Keyword(s):  
Least Action ◽  
Principle Of Least Action ◽  
Thermodynamic Processes

The purpose of this reply is to provide a discussion and closure for the comment paper by Dr. Bormashenko on the present authors’ article, which discussed the application of the principle of least action in reversible thermodynamic processes and cycles. Dr. Bormashenko’s questions and misunderstandings are responded to, and the differences between the present authors’ work and Lucia’s are also presented.

On the Shoulders of Giants

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Eighteenth Century ◽  
Robert Hooke ◽  
New Approach ◽  
Isaac Newton ◽  
Least Action ◽  
New Science ◽  
Principle Of Least Action ◽  
Parabolic Trajectory ◽  
Leonhard Euler ◽  
New Generation

Galileo’s parabolic trajectory launched a new approach to physics that was taken up by a new generation of scientists like Isaac Newton, Robert Hooke and Edmund Halley. The English Newtonian tradition was adopted by ambitious French iconoclasts who championed Newton over their own Descartes. Chief among these was Pierre Maupertuis, whose principle of least action was developed by Leonhard Euler and Joseph Lagrange into a rigorous new science of dynamics. Along the way, Maupertuis became embroiled in a famous dispute that entangled the King of Prussia as well as the volatile Voltaire who was mourning the death of his mistress Emilie du Chatelet, the lone female French physicist of the eighteenth century.

scholarly journals Nonlinear vibrations and time delay control of an extensible slowly rotating beam

2020 ◽  
Author(s):  
Jerzy Warminski ◽  
Lukasz Kloda ◽  
Jaroslaw Latalski ◽  
Andrzej Mitura ◽  
Marcin Kowalczuk
Keyword(s):  
Time Delay ◽  
Control Strategies ◽  
Vibration Reduction ◽  
Least Action ◽  
Active Elements ◽  
Principle Of Least Action ◽  
Second Mode ◽  
Delay Control ◽  
Speed Range ◽  
System With Time Delay

AbstractNonlinear dynamics of a rotating flexible slender beam with embedded active elements is studied in the paper. Mathematical model of the structure considers possible moderate oscillations thus the motion is governed by the extended Euler–Bernoulli model that incorporates a nonlinear curvature and coupled transversal–longitudinal deformations. The Hamilton’s principle of least action is applied to derive a system of nonlinear coupled partial differential equations (PDEs) of motion. The embedded active elements are used to control or reduce beam oscillations for various dynamical conditions and rotational speed range. The control inputs generated by active elements are represented in boundary conditions as non-homogenous terms. Classical linear proportional (P) control and nonlinear cubic (C) control as well as mixed ($$P-C$$ P - C ) control strategies with time delay are analyzed for vibration reduction. Dynamics of the complete system with time delay is determined analytically solving directly the PDEs by the multiple timescale method. Natural and forced vibrations around the first and the second mode resonances demonstrating hardening and softening phenomena are studied. An impact of time delay linear and nonlinear control methods on vibration reduction for different angular speeds is presented.

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

Application of principle of least action to beam problems

2000 ◽  
Vol 142 (1-4) ◽  
pp. 235-243 ◽  
Author(s):  
B. Tabarrok ◽  
W. L. Cleghorn
Keyword(s):  
Least Action ◽  
Principle Of Least Action

scholarly journals Evaluation of Functioning Quality of Local Electrical Systems by the Criterion Method Based on Markov Processes

2019 ◽  
pp. 169-172 ◽  
Author(s):  
Petro Lezhniuk ◽  
Vyacheslav Komar ◽  
Natalya Sobchuk ◽  
Olena Sikorska
Keyword(s):  
Markov Processes ◽  
Renewable Energy Sources ◽  
Network Development ◽  
Least Action ◽  
Electrical Systems ◽  
Principle Of Least Action ◽  
Intensive Development ◽  
Criterion Method ◽  
The Ideal

The article proposes to use of a combination of the criterion method and Markov processes to evaluate the quality of functioning of renewable energy sources (RES) in the form of integrated readiness characteristic of the electricity network with RES or a local electrical system (LES). This is possible throughthe analysis of the problems of ensuring the quality of electricity supply in the conditions of intensive development of RES and defined by the qualimetric characteristics of the electricity networks, which are important for the provision of quality electricity. This contribute the development of generalizedsolutions and network development strategies, especially when it comes to building RES. The components of the integral index are determined as the probability of matching the actual regime to the "ideal". The "ideal" mode is determined on the basis of the principle of least action and corresponds to the circuit diagram of the network formed by the r-scheme. The basis thus determined in this way reduces the subjectivity of both evaluations and decisions taken on the basis of it.

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