Hamilton's principle of least action in nervous excitation

1989 ◽  
Vol 85 (6) ◽  
pp. 1463 ◽  
Author(s):  
Gerhard Dickel
Keyword(s):  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Least Action ◽  
Principle Of Least Action ◽  
Nervous Excitation

Hamiltonian Mechanics of Discrete Particle Systems

1994 ◽  
Author(s):  
Antony N. Beris ◽  
Brian J. Edwards
Keyword(s):  
Calculus Of Variations ◽  
Symplectic Structure ◽  
Mathematical Formulation ◽  
Real Variable ◽  
Simple Problem ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Dynamical Equations ◽  
Least Action ◽  
Principle Of Least Action

In the previous chapter, we discussed briefly the fundamental nature of the symplectic structure of theories in optics in order to illustrate the underlying uniformity, physical consistency, and mathematical simplicity inherent to a symplectic mathematical formulation of the governing equations. Hence the main emphasis of chapter 2 was to “discover” the symplectic structure in the physical theories of optics and to see how this structure is interconnected with and implies fundamental theorems in optics, such as Fermat's principle and Hamilton's equations. In the present chapter, we continue our efforts to present a coherent description of symplectic transformations and their applications to physical systems; however, here we switch our emphasis from the underlying symplectic structure of the dynamical equations to the physical integrity of the Poisson bracket and the canonical equations which find their roots in Hamilton's principle of least action and the calculus of variations. Hence we intend to cover ground in this chapter which we neglected in the previous one, and, in so doing, to gradually begin to move towards the applications of the extended bracket formalism at which this book is aimed. In order to apply Hamilton's principle of least action, we first need to study a simple problem of the calculus of variations, following Bedford [1985, §1.1]. Let x be a real variable (x∊ R) on the closed interval x1≤ x≤ x2, denoted [x1 ,x2] .

Fermat’s Principle and Hamilton’s Principle: Does a least action take a least time for happening?

2019 ◽  
Author(s):  
Miftachul Hadi
Keyword(s):  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Least Action ◽  
Fermat’S Principle ◽  
Fermat's Principle

We explore deeper and analyse in more detail Fermat’s and Hamilton’s principles. We try to address some questions: Is it possible to have δS negative? Is Hamilton’s principle always valid for entire path of the system? Is there a relation between Fermat’s principle and Hamilton’s principle? We assume analogy with Hamilton’s principle, is Fermat’s principle always valid for entire path of the system? Does a least action take a least time for happening?

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.

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