The modern theory of classical mechanics, developed by Lagrange, Hamilton andNoether, attempts to cast all of classical motion in the form of anoptimization problem, based on an energy functional called the classicalaction. The most important advantage of this formalism is the ability tomanifestly incorporate and exploit symmetries and conservation laws. Thisreformulation succeeded for unconstrained and holonomic systems that at mostobey position equality constraints. Non-holonomic systems, which obey velocitydependent constraints or position inequality constraints, are abundant innature and of central relevance for science, engineering and industry. Allattempts so far to solve non-holonomic dynamics as a classical actionoptimization problem have failed. Here we utilize the classical limit of aquantum field theory action principle to construct a novel classical action fornon-holonomic systems. We therefore put to rest the 190 year old question ofwhether classical mechanics is variational, answering in the affirmative. Weillustrate and validate our approach by solving three canonical model problemsby direct numerical optimization of our new action. The formalism developed inthis work significantly extends the reach of action principles to a large classof relevant mechanical systems, opening new avenues for their analysis andcontrol both analytically and numerically.
{"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}
The current study explores the analysis of crack in initially stressed,rotating material strips, drawing insights from singular integral equations. Inthis work, a self-reinforced material strip with finite thickness and infiniteextent, subjected to initial stress and rotational motion, has been consideredto examine the Griffith fracture. The edges of the strip are pushed by constantloads from punches moving alongside it. This study makes waves in the materialthat affect the fracture's movement. A distinct mathematical technique isutilized to streamline the resolution of a pair of singular integral equationsfeaturing First-order singularities. These obtained equations help usunderstand how the fracture behaves. The force acting at the fracture's edge ismodeled using the Dirac delta function. Then, the Hilbert transformation methodcalculates the stress intensity factor (SIF) at the fracture's edge.Additionally, the study explores various scenarios, including constantintensity force without punch pressure, rotation parameter, initial stress, andisotropy in the strip, deduced from the SIF expression. Numerical computationsand graphical analyses are conducted to assess the influence of various factorson SIF in the study. Finally, a comparison is made between the behavior offractures in the initially stressed and rotating reinforced material strip andthose in a standard material strip to identify any differences.
{"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}
A relationship is established between the effective Youngs modulus of atwo-phase elastic composite and a known mathematical mean value. Specifically,the effective Youngs modulus of a composite obtained from repeated parallel andserial constructions is equal to the arithmetic-geometric mean of the Youngsmoduli of the component materials. This result also applies to electriccircuits with resistors in repeated parallel and serial connections.
{"title":"Effective Youngs Modulus of Two-Phase Elastic Composites by Repeated Isostrain and Isostress Constructions and Arithmetic-Geometric Mean","authors":"Jiashi Yang","doi":"arxiv-2409.09738","DOIUrl":"https://doi.org/arxiv-2409.09738","url":null,"abstract":"A relationship is established between the effective Youngs modulus of a\u0000two-phase elastic composite and a known mathematical mean value. Specifically,\u0000the effective Youngs modulus of a composite obtained from repeated parallel and\u0000serial constructions is equal to the arithmetic-geometric mean of the Youngs\u0000moduli of the component materials. This result also applies to electric\u0000circuits with resistors in repeated parallel and serial connections.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269309","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}
In mechanics, common energy principles are based on fixed boundaryconditions. However, in bridge engineering structures, it is usually necessaryto adjust the boundary conditions to make the structure's internal forcereasonable and save materials. However, there is currently little theoreticalresearch in this area. To solve this problem, this paper proposes the principleof minimum virtual work for movable boundaries in mechanics through theoreticalderivation such as variation method and tensor analysis. It reveals that theexact solution of the mechanical system minimizes the total virtual work of thesystem among all possible displacements, and the conclusion that the principleof minimum potential energy is a special case of this principle is obtained. Atthe same time, proposed virtual work boundaries and control conditions, whichadded to the fundamental equations of mechanics. The general formula ofmultidimensional variation method for movable boundaries is also proposed,which can be used to easily derive the basic control equations of themechanical system. The incremental method is used to prove the theory ofminimum value in multidimensional space, which extends the Pontryagin's minimumvalue principle. Multiple bridge examples were listed to demonstrate theextensive practical value of the theory presented in this article. The theoryproposed in this article enriches the energy principle and variation method,establishes fundamental equations of mechanics for the structural optimizationof movable boundary, and provides a path for active control of mechanicalstructures, which has important theoretical and engineering practicalsignificance.
{"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}
Exceptional points (EPs) are spectral singularities in non-Hermitian systemswhere eigenvalues and their corresponding eigenstates coalesce simultaneously.In this study, we calculate scattering poles in an open spherical solid andpropose a depth-first search-based method to identify EPs. Using the proposedmethod, we numerically identify multiple EPs in a parameter space and confirmthe simultaneous degeneracy of scattering poles through numerical experiments.The proposed method and findings enable the exploration of applications inpractical three-dimension models.
{"title":"Observation of exceptional points in a spherical open elastic system","authors":"Hiroaki Deguchi, Kei Matsushima, Takayuki Yamada","doi":"arxiv-2409.08560","DOIUrl":"https://doi.org/arxiv-2409.08560","url":null,"abstract":"Exceptional points (EPs) are spectral singularities in non-Hermitian systems\u0000where eigenvalues and their corresponding eigenstates coalesce simultaneously.\u0000In this study, we calculate scattering poles in an open spherical solid and\u0000propose a depth-first search-based method to identify EPs. Using the proposed\u0000method, we numerically identify multiple EPs in a parameter space and confirm\u0000the simultaneous degeneracy of scattering poles through numerical experiments.\u0000The proposed method and findings enable the exploration of applications in\u0000practical three-dimension models.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259841","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}
Symmetries -- whether explicit, latent, or hidden -- are fundamental tounderstanding topological materials. This work introduces a prototypicalspring-mass model that extends beyond established canonical models, revealingtopological edge states with distinct profiles at opposite edges. These edgestates originate from hidden symmetries that become apparent only indeformation coordinates, as opposed to the conventional displacementcoordinates used for bulk-boundary correspondence. Our model realized throughthe intricate connectivity of a spinner chain, demonstrates experimentallydistinct edge states at opposite ends. By extending this framework to twodimensions, we explore the conditions required for such edge waves and theirhidden symmetry in deformation coordinates. We also show that these edge statesare robust against disorders that respect the hidden symmetry. This researchpaves the way for advanced material designs with tailored boundary conditionsand edge state profiles, offering potential applications in fields such asphotonics, acoustics, and mechanical metamaterials.
{"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}
It is shown that when the well-known minimal complementary energy variationalprinciple in linear elastostatics is written in a different form with thestrain tensor as an independent variable and the constitutive relation as oneof the constraints, the removal of the constraints by Lagrange multipliersleads to a three-field variational principle with the displacement vector,stress field and strain field as independent variables. This three-fieldvariational principle is without constrains and its variational functional isdifferent from those of the existing three-field variational principles. Thegeneralization is not unique. The procedure is mathematical and may be used inother branches of physics.
{"title":"On Generalizations of the Minimal Complementary Energy Variational Principle in Linear Elastostatics","authors":"Jiashi Yang","doi":"arxiv-2409.06875","DOIUrl":"https://doi.org/arxiv-2409.06875","url":null,"abstract":"It is shown that when the well-known minimal complementary energy variational\u0000principle in linear elastostatics is written in a different form with the\u0000strain tensor as an independent variable and the constitutive relation as one\u0000of the constraints, the removal of the constraints by Lagrange multipliers\u0000leads to a three-field variational principle with the displacement vector,\u0000stress field and strain field as independent variables. This three-field\u0000variational principle is without constrains and its variational functional is\u0000different from those of the existing three-field variational principles. The\u0000generalization is not unique. The procedure is mathematical and may be used in\u0000other branches of physics.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186291","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}
It is generally assumed that the retarded Lienard-Wiechert electromagneticfield produced by a point particle depends on the acceleration of that sourceparticle. This dependence is not real, it is an illusion. The trueelectromagnetic interaction is time symmetric (half retarded and half advanced)and depends only on the positions and velocities of the electrically chargedparticles. A different acceleration of the retarded source particle will resultin a different position and velocity of the advanced source particle, changingin this way the Lorentz force felt by the test particle.
{"title":"The illusion of acceleration in the retarded Lienard-Wiechert electromagnetic field","authors":"Calin Galeriu","doi":"arxiv-2409.05338","DOIUrl":"https://doi.org/arxiv-2409.05338","url":null,"abstract":"It is generally assumed that the retarded Lienard-Wiechert electromagnetic\u0000field produced by a point particle depends on the acceleration of that source\u0000particle. This dependence is not real, it is an illusion. The true\u0000electromagnetic interaction is time symmetric (half retarded and half advanced)\u0000and depends only on the positions and velocities of the electrically charged\u0000particles. A different acceleration of the retarded source particle will result\u0000in a different position and velocity of the advanced source particle, changing\u0000in this way the Lorentz force felt by the test particle.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186293","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}
Ansgar SiemensZentrum für Optische Quantentechnologien, Fachbereich Physik, Universität Hamburg, Peter SchmelcherZentrum für Optische Quantentechnologien, Fachbereich Physik, Universität HamburgHamburg Center for Ultrafast Imaging, Universität Hamburg
We explore the scattering dynamics of classical Coulomb-interacting clustersof ions confined to a helical geometry. Ion clusters of equally chargedparticles constrained to a helix can form many-body bound states, i.e. theyexhibit stable motion of Coulomb-interacting identical ions. We analyze thescattering and fragmentation behavior of two ion clusters, therebyunderstanding the rich phenomenology of their dynamics. The scattering dynamicsis complex in the sense that it exhibits cascades of decay processes involvingstrongly varying cluster sizes. These processes are governed by the internalenergy flow and the underlying oscillatory many-body potential. We specificallyfocus on the impact of the collision energy on the dynamics of individual ionsduring and immediately after the collision of two clusters, and on the internaldynamics of ion clusters that are excited during a cluster collision.
{"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}
David Cichra, Vít Průša, K. R. Rajagopal, Casey Rodriguez, Martin Vejvoda
The concept of "effective mass" is frequently used for the simplification ofcomplex lumped parameter systems (discrete dynamical systems) as well asmaterials that have complicated microstructural features. From the perspectiveof wave propagation, it is claimed that for some bodies described asmetamaterials, the corresponding "effective mass" can be frequency dependent,negative or it may not even be a scalar quantity. The procedure has even ledsome authors to suggest that Newton's second law needs to be modified withinthe context of classical continuum mechanics. Such absurd physical conclusionsare a consequence of appealing to the notion of "effective mass" with apreconception for the constitutive structure of the metamaterial and using acorrect mathematical procedure. We show that such unreasonable physicalconclusions would not arise if we were to use the appropriate "effectiveconstitutive relation" for the metamaterial, rather than use the concept of"effective mass" with an incorrect predetermined constitutive relation.
{"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}
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