On the Least Action Principle – Hamiltonian Dynamics on Fixed Energy Levels in the Non-convex Case

2006 ◽  
Vol 6 (2) ◽  
Author(s):  
Roberto Giambò ◽  
Fabio Giannoni ◽  
Paolo Piccione
Keyword(s):  
Hamiltonian Dynamics ◽  
Energy Levels ◽  
General Context ◽  
Homogeneous Type ◽  
Least Action Principle ◽  
Least Action ◽  
Fixed Energy ◽  
The Least Action Principle ◽  
Convex Case ◽  
Classical Principle

AbstractWe review the classical Principle of the Least Action in a general context where the Hamilton functionH is possibly non-convex. We show how the van Groesen [6] principle follows as a particular case where H is hyperregular and of homogeneous type. Homogeneous scalar field spacetimes in spherical symmetry are derived as an application.

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.

Lagrange formalism in field theory

2021 ◽  
pp. 31-41
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Field Theory ◽  
Classical Field Theory ◽  
Momentum Tensor ◽  
Subsequent Treatment ◽  
Classical Field ◽  
Least Action Principle ◽  
Least Action ◽  
Field System ◽  
The Least Action Principle ◽  
Lagrange Formalism

This chapter is devoted to a general discussion of classical field theory. It presents the minimum information required about classical fields for the subsequent treatment of quantum theory in the rest of the book. The Lagrange formalism for the fields is introduced, based on the least action principle. Global symmetries are described, and the proof of Noether's theorem given. In addition, the energy-momentum tensor for a field system is constructed as an example.

scholarly journals On the free time minimizers of the NewtonianN-body problem

2013 ◽  
Vol 156 (2) ◽  
pp. 209-227 ◽  
Author(s):  
ADRIANA DA LUZ ◽  
EZEQUIEL MADERNA
Keyword(s):  
Special Class ◽  
Body Problem ◽  
Free Time ◽  
Global Minimization ◽  
Kam Theorem ◽  
Least Action Principle ◽  
Least Action ◽  
Homothetic Motion ◽  
The Least Action Principle ◽  
Minimization Property

AbstractIn this paper we study the existence and the dynamics of a very special class of motions, which satisfy a strong global minimization property. More precisely, we call a free time minimizer a curve which satisfies the least action principle between any pair of its points without the constraint of time for the variations. An example of a free time minimizer defined on an unbounded interval is a parabolic homothetic motion by a minimal central configuration. The existence of a large amount of free time minimizers can be deduced from the weak KAM theorem. In particular, for any choice ofx0, there should be at least one free time minimizerx(t)defined for allt≥ 0 and satisfyingx(0)=x0. We prove that such motions are completely parabolic. Using Marchal's theorem we deduce as a corollary that there are no entire free time minimizers, i.e. defined on$\mathbb{R}$. This means that the Mañé set of the NewtonianN-body problem is empty.

Hydrodynamical description of the continuous Heisenberg chain

1981 ◽  
Vol 59 (4) ◽  
pp. 511-514 ◽  
Author(s):  
Lukasz A. Turski
Keyword(s):  
Canonical Formalism ◽  
Finite Amplitude ◽  
Heisenberg Chain ◽  
Wave Excitation ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Spin Wave Excitation ◽  
Hydrodynamical Description ◽  
Dynamical Properties

The dynamical properties of a continuous Heisenberg chain (CHC) are analysed by means of the Lakshmanan variables. The least action principle for CHC is proposed and canonical formalism constructed following standard procedures.The instability of a finite amplitude spin wave excitation of the chain is analysed as an illustrative example.

Existence of periodic solutions for sublinear second order dynamical system with (q, p)-Laplacian

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Xiaoxia Yang ◽  
Haibo Chen
Keyword(s):  
Dynamical System ◽  
Saddle Point ◽  
Periodic Solutions ◽  
Existence Theorems ◽  
Second Order ◽  
Saddle Point Theorem ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Existence Of Periodic Solutions

AbstractIn this paper, some existence theorems are obtained for periodic solutions of second order dynamical system with (q, p)-Laplaician by using the least action principle and the saddle point theorem. Our results improve Pasca and Tang’ results.

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

scholarly journals Constructions of f(R,G,𝒯) gravity from some expansions of the Universe

2020 ◽  
Vol 35 (31) ◽  
pp. 2050203
Author(s):  
Ujjal Debnath
Keyword(s):  
Energy Conditions ◽  
Energy Tensor ◽  
De Sitter ◽  
Field Equations ◽  
Least Action Principle ◽  
Future Singularity ◽  
Least Action ◽  
The Least Action Principle ◽  
Modified Gravity Theory ◽  
Stress Energy

Here we propose the extended modified gravity theory named [Formula: see text] gravity where [Formula: see text] is the Ricci scalar, [Formula: see text] is the Gauss–Bonnet invariant, and [Formula: see text] is the trace of the stress-energy tensor. We derive the gravitational field equations in [Formula: see text] gravity by taking the least action principle. Next we construct the [Formula: see text] in terms of [Formula: see text], [Formula: see text] and [Formula: see text] in de Sitter as well as power-law expansion. We also construct [Formula: see text] if the expansion follows the finite-time future singularity (big rip singularity). We investigate the energy conditions in this modified theory of gravity and examine the validity of all energy conditions.

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