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.

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.

Least Action Principle for Mem-Elements

2015 ◽  
Vol 24 (10) ◽  
pp. 1550148 ◽  
Author(s):  
Wieslaw Marszalek ◽  
Tewodros Amdeberhan
Keyword(s):  
Natural Environment ◽  
Action Principle ◽  
Least Action Principle ◽  
Least Action ◽  
Full Characterization ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Modern Physics ◽  
Stationary Action

We study the principle of least (stationary) action for mem-elements. The least action principle allows us to derive relationships between the electrical variables for each of the six mem-elements. The principle of least action from modern physics is a natural environment to characterize mem-elements, including various one-period loops in the context of periodic circuits. The time-integrals of Lagrangian lead to the action and coaction quantities and a full characterization of mem-elements with periodic control variables.

scholarly journals Least action principle and gravitational double layer

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040002 ◽  
Author(s):  
Victor Berezin ◽  
Vyacheslav Dokuchaev ◽  
Yury Eroshenko ◽  
Alexei Smirnov
Keyword(s):  
Shock Wave ◽  
Double Layer ◽  
Equations Of Motion ◽  
Action Principle ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Higher Derivative ◽  
Gravitational Theories ◽  
New Phenomena

The higher derivative gravitational theories exhibit new phenomena absent in General Relativity. One of them is the possible formation of the so called double layer which is the pure gravitational phenomenon and can be interpreted, in a sense, as the gravitational shock wave. In this paper we show how some very important features of the double layer equations of motion can be extracted straight from the least action principle.

An Observation on Least Action Principle in Classical Mechanics Oriented on the Evaluation of Relativistic Error Concerning the Measurements of Light Propagating in a Liquid

2011 ◽  
Vol 1 (3) ◽  
pp. 14-24 ◽  
Author(s):  
Alessandro Massaro ◽  
Piero Adriano Massaro
Keyword(s):  
Euler Equations ◽  
Classical Mechanics ◽  
First Integrals ◽  
Action Principle ◽  
Classical Approach ◽  
Limit Case ◽  
Least Action Principle ◽  
Calculus Of Variation ◽  
Least Action ◽  
Approximate First Integrals

The authors prove that the standard least action principle implies a more general form of the same principle by which they can state generalized motion equation including the classical Euler equation as a particular case. This form is based on an observation regarding the last action principle about the limit case in the classical approach using symmetry violations. Furthermore the well known first integrals of the classical Euler equations become only approximate first integrals. The authors also prove a generalization of the fundamental lemma of the calculus of variation and we consider the application in electromagnetism.

scholarly journals Extended harmonic mapping connects the equations in classical, statistical, fluid, quantum physics and general relativity

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Xiaobo Zhai ◽  
Changyu Huang ◽  
Gang Ren
Keyword(s):  
General Relativity ◽  
Quantum Physics ◽  
Harmonic Maps ◽  
Classical Mechanics ◽  
Harmonic Mapping ◽  
Geodesic Equation ◽  
Lagrange Equations ◽  
Least Action ◽  
Principle Of Least Action ◽  
Fundamental Equations

Abstract One potential pathway to find an ultimate rule governing our universe is to hunt for a connection among the fundamental equations in physics. Recently, Ren et al. reported that the harmonic maps with potential introduced by Duan, named extended harmonic mapping (EHM), connect the equations of general relativity, chaos and quantum mechanics via a universal geodesic equation. The equation, expressed as Euler–Lagrange equations on the Riemannian manifold, was obtained from the principle of least action. Here, we further demonstrate that more than ten fundamental equations, including that  of classical mechanics, fluid physics, statistical physics, astrophysics, quantum physics and general relativity, can be connected by the same universal geodesic equation. The connection sketches a family tree of the physics equations, and their intrinsic connections reflect an alternative ultimate rule of our universe, i.e., the principle of least action on a Finsler manifold.

scholarly journals Predicting the peculiar velocities of nearby PSCz galaxies using the Least Action Principle

2001 ◽  
Vol 322 (1) ◽  
pp. 121-130 ◽  
Author(s):  
J. Sharpe ◽  
M. Rowan-Robinson ◽  
A. Canavezes ◽  
W. Saunders ◽  
E. Branchini ◽  
...  
Keyword(s):  
Action Principle ◽  
Least Action Principle ◽  
Least Action ◽  
Peculiar Velocities ◽  
The Least Action Principle

The Definition of Aesthetics and Beauty

2020 ◽  
pp. 157-178
Keyword(s):  
Action Principle ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Natural Beauty ◽  
The World ◽  
Definition Of

This chapter proposes the definition of beauty and discusses the levels of beauty and the structure of beauty. This chapter points out that Aesthetics should be a science that studies beauty in general, including natural beauty, artistic beauty, design beauty, and aesthetic feelings. Beauty, just like material and thinking, is the foundation of everything, without which the world won't even exist. Beauty is an evolutionary existence, an objective and natural existence, and an existence of emergence. It is hierarchical, structural, and dynamic, and its core is the “least action principle”.

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