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.

The Principle of Least Action

2018 ◽  
pp. 134-157
Author(s):  
Yemima Ben-Menahem
Keyword(s):  
Gottfried Wilhelm Leibniz ◽  
Action Principle ◽  
Least Action Principle ◽  
Baruch Spinoza ◽  
Isaac Newton ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Leonhard Euler ◽  
Probabilistic Context

This chapter examines the place of the “least action” principle in the causal family and its role in in modern science's transition from teleology to causality. It first provides an overview of the principle of sufficient reason, which illustrates the intricate relations between reasons and causes in the seventeenth theory, along with various conceptions of God proposed by thinkers such as Gottfried Wilhelm Leibniz, Baruch Spinoza, Isaac Newton, and René Descartes. The chapter then considers the work of Leonhard Euler and Pierre-Louis Moreau de Maupertuis on the least action principle. Finally, it analyzes the least action principle's reappearance in the probabilistic context of quantum mechanics, taking into account Richard Feynman's ingenious solution to the long-standing philosophical problem of teleology in physics.

Antecedents

2017 ◽  
Author(s):  
Jennifer Coopersmith
Keyword(s):  
Eighteenth Century ◽  
Energy Analysis ◽  
Force Analysis ◽  
Isoperimetric Problems ◽  
Least Action ◽  
Quantitative Test ◽  
Perpetual Motion ◽  
Galilean Relativity ◽  
Principle Of Least Action ◽  
Variational Mechanics

Early ideas about optimization principles were brought in by an eclectic group of extraordinary thinkers: the Ancients (Hero, and Princess Dido), Fermat with his Principle of Least Time, the Bernoullis, Leibniz, Maupertuis, Euler, and d’Alembert. Also, Stevin was the first to invoke the impossibility of perpetual motion in a proof, and Huygens was the first to put Galilean Relativity to a quantitative test. The Swiss family of mathematical geniuses, the Bernoullis, tackled isoperimetric problems, such as the brachystochrone, and Johann Bernoulli discovered the Principle of Virtual Velocities. The flavour of the eighteenth century is shown in the evocative tale of the König affair, and the correspondence between Daniel Bernoulli and Euler. It is shown how symmetry arguments, leading ultimately to an energy-analysis, were competing with Newton’s force-analysis. The Principle of Least Action and Variational Mechanics, proper, were developed by Lagrange, Hamilton, and Jacobi.

The Curious Eye

2020 ◽  
Author(s):  
Erin Webster
Keyword(s):  
Seventeenth Century ◽  
Human Vision ◽  
Francis Bacon ◽  
Robert Hooke ◽  
Robert Boyle ◽  
Isaac Newton ◽  
Johannes Kepler ◽  
The Social ◽  
The Subject ◽  
Historical Moment

The Curious Eye explores early modern debates over two related questions: what are the limits of human vision, and to what extent can these limits be overcome by technological enhancement? Today, in our everyday lives we rely on optical technology to provide us with information about visually remote spaces even as we question the efficacy and ethics of such pursuits. But the debates surrounding the subject of technologically mediated vision have their roots in a much older literary tradition in which the ability to see beyond the limits of natural human vision is associated with philosophical and spiritual insight as well as social and political control. The Curious Eye provides insight into the subject of optically mediated vision by returning to the literature of the seventeenth century, the historical moment in which human visual capacity in the West was first extended through the application of optical technologies to the eye. Bringing imaginative literary works by Francis Bacon, John Milton, Margaret Cavendish, and Aphra Behn together with optical and philosophical treatises by Johannes Kepler, René Descartes, Robert Hooke, Robert Boyle, and Isaac Newton, The Curious Eye explores the social and intellectual impact of the new optical technologies of the seventeenth century on its literature. At the same time, it demonstrates that social, political, and literary concerns are not peripheral to the optical science of the period but rather an integral part of it, the legacy of which we continue to experience.

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.

Deconstructing female conventions

2006 ◽  
Vol 33 (1-2) ◽  
pp. 11-38 ◽  
Author(s):  
Maria E. Rodríguez-Gil
Keyword(s):  
Eighteenth Century ◽  
Public Sphere ◽  
Mother Tongue ◽  
New Approach ◽  
The Public ◽  
English Grammar ◽  
The Public Sphere ◽  
At Home

Summary This paper examines Ann Fisher’s (1719–1778) most important and influential work, A New Grammar (1745?). In this grammar, the author did not follow the trend of making English grammar fit the Latin pattern, a common practice still in the eighteenth century. Instead, she wrote an English grammar based on the nature and observation of her mother tongue. Besides, she scattered throughout her grammar a wide set of teaching devices, the ‘examples of bad English’ being her most important contribution. Her innovations and her new approach to the description of English grammar were indeed welcomed by contemporary readers, since her grammar saw almost forty editions and reprints, it influenced other grammarians, for instance Thomas Spence (1750–1814), and it reached other markets, such as London. In order to understand more clearly the value of this grammar and of its author, this grammar has to be seen in the context of her life. For this reason, we will also discuss some details of her unconventional lifestyle: unconventional in the sense that she led her life in the public sphere, not happy with the prevailing idea that women should be educated for a life at home.

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
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