Time-domain formulation of electromagnetic scattering based on a polarization-mode expansion and the principle of least action

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.

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Transient Electromagnetic Scattering from Bodies of Revolution by Time-Domain Combined Field Integral Equation

IET International Radar Conference 2015 ◽

10.1049/cp.2015.1127 ◽

2015 ◽

Author(s):

Z. He ◽

Y.Z. Sun ◽

D.W. Song ◽

Z.H. Fan ◽

D.Z. Ding ◽

...

Keyword(s):

Integral Equation ◽

Time Domain ◽

Electromagnetic Scattering ◽

Bodies Of Revolution ◽

Transient Electromagnetic ◽

Field Integral

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

Nonlinear Dynamics ◽

10.1007/s11071-020-06079-3 ◽

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.

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A least action principle for interceptive walking

Scientific Reports ◽

10.1038/s41598-021-81722-6 ◽

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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