arXiv - PHYS - Classical Physics最新文献

A Unifying Action Principle for Classical Mechanical Systems 经典力学系统的统一作用原理

arXiv - PHYS - Classical Physics Pub Date : 2024-09-17 DOI: arxiv-2409.11063

A. Rothkopf, W. A. Horowitz

{"title":"A Unifying Action Principle for Classical Mechanical Systems","authors":"A. Rothkopf, W. A. Horowitz","doi":"arxiv-2409.11063","DOIUrl":"https://doi.org/arxiv-2409.11063","url":null,"abstract":"The modern theory of classical mechanics, developed by Lagrange, Hamilton and\u0000Noether, attempts to cast all of classical motion in the form of an\u0000optimization problem, based on an energy functional called the classical\u0000action. The most important advantage of this formalism is the ability to\u0000manifestly incorporate and exploit symmetries and conservation laws. This\u0000reformulation succeeded for unconstrained and holonomic systems that at most\u0000obey position equality constraints. Non-holonomic systems, which obey velocity\u0000dependent constraints or position inequality constraints, are abundant in\u0000nature and of central relevance for science, engineering and industry. All\u0000attempts so far to solve non-holonomic dynamics as a classical action\u0000optimization problem have failed. Here we utilize the classical limit of a\u0000quantum field theory action principle to construct a novel classical action for\u0000non-holonomic systems. We therefore put to rest the 190 year old question of\u0000whether classical mechanics is variational, answering in the affirmative. We\u0000illustrate and validate our approach by solving three canonical model problems\u0000by direct numerical optimization of our new action. The formalism developed in\u0000this work significantly extends the reach of action principles to a large class\u0000of relevant mechanical systems, opening new avenues for their analysis and\u0000control both analytically and numerically.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Crack Dynamics in Rotating, Initially Stressed Material Strips: A Mathematical Approach 旋转初始应力材料带的裂缝动力学：数学方法

arXiv - PHYS - Classical Physics Pub Date : 2024-09-15 DOI: arxiv-2409.11434

Soniya Chaudhary, Diksha, Pawan Kumar Sharma

{"title":"Crack Dynamics in Rotating, Initially Stressed Material Strips: A Mathematical Approach","authors":"Soniya Chaudhary, Diksha, Pawan Kumar Sharma","doi":"arxiv-2409.11434","DOIUrl":"https://doi.org/arxiv-2409.11434","url":null,"abstract":"The current study explores the analysis of crack in initially stressed,\u0000rotating material strips, drawing insights from singular integral equations. In\u0000this work, a self-reinforced material strip with finite thickness and infinite\u0000extent, subjected to initial stress and rotational motion, has been considered\u0000to examine the Griffith fracture. The edges of the strip are pushed by constant\u0000loads from punches moving alongside it. This study makes waves in the material\u0000that affect the fracture's movement. A distinct mathematical technique is\u0000utilized to streamline the resolution of a pair of singular integral equations\u0000featuring First-order singularities. These obtained equations help us\u0000understand how the fracture behaves. The force acting at the fracture's edge is\u0000modeled using the Dirac delta function. Then, the Hilbert transformation method\u0000calculates the stress intensity factor (SIF) at the fracture's edge.\u0000Additionally, the study explores various scenarios, including constant\u0000intensity force without punch pressure, rotation parameter, initial stress, and\u0000isotropy in the strip, deduced from the SIF expression. Numerical computations\u0000and graphical analyses are conducted to assess the influence of various factors\u0000on SIF in the study. Finally, a comparison is made between the behavior of\u0000fractures in the initially stressed and rotating reinforced material strip and\u0000those in a standard material strip to identify any differences.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"210 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Effective Youngs Modulus of Two-Phase Elastic Composites by Repeated Isostrain and Isostress Constructions and Arithmetic-Geometric Mean 通过重复等应变和等应力构造以及算术几何平均数计算两相弹性复合材料的有效杨氏模量

arXiv - PHYS - Classical Physics Pub Date : 2024-09-15 DOI: arxiv-2409.09738

Jiashi Yang

引用次数: 0

The principle of minimum virtual work and its application in bridge engineering 最小虚功原理及其在桥梁工程中的应用

arXiv - PHYS - Classical Physics Pub Date : 2024-09-14 DOI: arxiv-2409.11431

Lukai Xiang

{"title":"The principle of minimum virtual work and its application in bridge engineering","authors":"Lukai Xiang","doi":"arxiv-2409.11431","DOIUrl":"https://doi.org/arxiv-2409.11431","url":null,"abstract":"In mechanics, common energy principles are based on fixed boundary\u0000conditions. However, in bridge engineering structures, it is usually necessary\u0000to adjust the boundary conditions to make the structure's internal force\u0000reasonable and save materials. However, there is currently little theoretical\u0000research in this area. To solve this problem, this paper proposes the principle\u0000of minimum virtual work for movable boundaries in mechanics through theoretical\u0000derivation such as variation method and tensor analysis. It reveals that the\u0000exact solution of the mechanical system minimizes the total virtual work of the\u0000system among all possible displacements, and the conclusion that the principle\u0000of minimum potential energy is a special case of this principle is obtained. At\u0000the same time, proposed virtual work boundaries and control conditions, which\u0000added to the fundamental equations of mechanics. The general formula of\u0000multidimensional variation method for movable boundaries is also proposed,\u0000which can be used to easily derive the basic control equations of the\u0000mechanical system. The incremental method is used to prove the theory of\u0000minimum value in multidimensional space, which extends the Pontryagin's minimum\u0000value principle. Multiple bridge examples were listed to demonstrate the\u0000extensive practical value of the theory presented in this article. The theory\u0000proposed in this article enriches the energy principle and variation method,\u0000establishes fundamental equations of mechanics for the structural optimization\u0000of movable boundary, and provides a path for active control of mechanical\u0000structures, which has important theoretical and engineering practical\u0000significance.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Observation of exceptional points in a spherical open elastic system 球形开放弹性系统中的异常点观测

arXiv - PHYS - Classical Physics Pub Date : 2024-09-13 DOI: arxiv-2409.08560

Hiroaki Deguchi, Kei Matsushima, Takayuki Yamada

引用次数: 0

Edge States with Hidden Topology in Spinner Lattices 旋转晶格中具有隐藏拓扑结构的边缘状态

arXiv - PHYS - Classical Physics Pub Date : 2024-09-12 DOI: arxiv-2409.07949

Udbhav Vishwakarma, Murthaza Irfan, Georgios Theocharis, Rajesh Chaunsali

{"title":"Edge States with Hidden Topology in Spinner Lattices","authors":"Udbhav Vishwakarma, Murthaza Irfan, Georgios Theocharis, Rajesh Chaunsali","doi":"arxiv-2409.07949","DOIUrl":"https://doi.org/arxiv-2409.07949","url":null,"abstract":"Symmetries -- whether explicit, latent, or hidden -- are fundamental to\u0000understanding topological materials. This work introduces a prototypical\u0000spring-mass model that extends beyond established canonical models, revealing\u0000topological edge states with distinct profiles at opposite edges. These edge\u0000states originate from hidden symmetries that become apparent only in\u0000deformation coordinates, as opposed to the conventional displacement\u0000coordinates used for bulk-boundary correspondence. Our model realized through\u0000the intricate connectivity of a spinner chain, demonstrates experimentally\u0000distinct edge states at opposite ends. By extending this framework to two\u0000dimensions, we explore the conditions required for such edge waves and their\u0000hidden symmetry in deformation coordinates. We also show that these edge states\u0000are robust against disorders that respect the hidden symmetry. This research\u0000paves the way for advanced material designs with tailored boundary conditions\u0000and edge state profiles, offering potential applications in fields such as\u0000photonics, acoustics, and mechanical metamaterials.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Generalizations of the Minimal Complementary Energy Variational Principle in Linear Elastostatics 论线性弹性力学中最小互补能量变分原理的一般化

arXiv - PHYS - Classical Physics Pub Date : 2024-09-10 DOI: arxiv-2409.06875

Jiashi Yang

引用次数: 0

The illusion of acceleration in the retarded Lienard-Wiechert electromagnetic field 延缓的李纳德-维切特电磁场中的加速幻觉

arXiv - PHYS - Classical Physics Pub Date : 2024-09-09 DOI: arxiv-2409.05338

Calin Galeriu

引用次数: 0

Classical scattering and fragmentation of clusters of ions in helical confinement 螺旋约束下离子簇的经典散射和碎裂

arXiv - PHYS - Classical Physics Pub Date : 2024-09-07 DOI: arxiv-2409.04852

Ansgar SiemensZentrum für Optische Quantentechnologien, Fachbereich Physik, Universität Hamburg, Peter SchmelcherZentrum für Optische Quantentechnologien, Fachbereich Physik, Universität HamburgHamburg Center for Ultrafast Imaging, Universität Hamburg

{"title":"Classical scattering and fragmentation of clusters of ions in helical confinement","authors":"Ansgar SiemensZentrum für Optische Quantentechnologien, Fachbereich Physik, Universität Hamburg, Peter SchmelcherZentrum für Optische Quantentechnologien, Fachbereich Physik, Universität HamburgHamburg Center for Ultrafast Imaging, Universität Hamburg","doi":"arxiv-2409.04852","DOIUrl":"https://doi.org/arxiv-2409.04852","url":null,"abstract":"We explore the scattering dynamics of classical Coulomb-interacting clusters\u0000of ions confined to a helical geometry. Ion clusters of equally charged\u0000particles constrained to a helix can form many-body bound states, i.e. they\u0000exhibit stable motion of Coulomb-interacting identical ions. We analyze the\u0000scattering and fragmentation behavior of two ion clusters, thereby\u0000understanding the rich phenomenology of their dynamics. The scattering dynamics\u0000is complex in the sense that it exhibits cascades of decay processes involving\u0000strongly varying cluster sizes. These processes are governed by the internal\u0000energy flow and the underlying oscillatory many-body potential. We specifically\u0000focus on the impact of the collision energy on the dynamics of individual ions\u0000during and immediately after the collision of two clusters, and on the internal\u0000dynamics of ion clusters that are excited during a cluster collision.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The conclusion that metamaterials could have negative mass is a consequence of improper constitutive characterisation 超材料可能具有负质量的结论是不恰当的构成特征描述的结果

arXiv - PHYS - Classical Physics Pub Date : 2024-09-06 DOI: arxiv-2409.05906

David Cichra, Vít Průša, K. R. Rajagopal, Casey Rodriguez, Martin Vejvoda

{"title":"The conclusion that metamaterials could have negative mass is a consequence of improper constitutive characterisation","authors":"David Cichra, Vít Průša, K. R. Rajagopal, Casey Rodriguez, Martin Vejvoda","doi":"arxiv-2409.05906","DOIUrl":"https://doi.org/arxiv-2409.05906","url":null,"abstract":"The concept of \"effective mass\" is frequently used for the simplification of\u0000complex lumped parameter systems (discrete dynamical systems) as well as\u0000materials that have complicated microstructural features. From the perspective\u0000of wave propagation, it is claimed that for some bodies described as\u0000metamaterials, the corresponding \"effective mass\" can be frequency dependent,\u0000negative or it may not even be a scalar quantity. The procedure has even led\u0000some authors to suggest that Newton's second law needs to be modified within\u0000the context of classical continuum mechanics. Such absurd physical conclusions\u0000are a consequence of appealing to the notion of \"effective mass\" with a\u0000preconception for the constitutive structure of the metamaterial and using a\u0000correct mathematical procedure. We show that such unreasonable physical\u0000conclusions would not arise if we were to use the appropriate \"effective\u0000constitutive relation\" for the metamaterial, rather than use the concept of\u0000\"effective mass\" with an incorrect predetermined constitutive relation.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"2022 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0