The motion of rockets is part of the study devoted to the motion of variable mass systems. Notably those in which the mass leaves permanently the considered system. Rockets are propelled forward by the reaction force produced by the hot exhausted gases ejected from their tales in the rearward direction. Thus their motion should not violate Newton's third principle of the equality of action and reaction forces during the exhaustion process. Nor should it violate Newton's second law of motion judged by inertial observers. However a close examination of the study of the motion of rockets in a major part of physics textbooks, if not all reveals erroneous determination of the expression of the thrust force that pushes the rocket in the forward direction. The false expression of the thrust force entails a bad effect on obtaining the right differential equation that governs the motion of rockets. This trap induced some prominent physics authors to pretend the in applicability of Newton's second law in such particular cases. Not only that, but they also modified Newton's second law in order to fit their purposes of obtaining the right differential equation, historically known under the name Tsiolkovsky rocket equation. The object of this paper is to give the true expression of the thrust force and to write the differential equation of motion of rockets without any necessity of modification of the classical laws. The paper also delves into the expression of the change of velocity of rockets, and proves that their motion is uniformly accelerated in the early stages of liftoff from the ground at condition of constant velocity of expulsion of hot gases from their nozzles.
{"title":"Rocket motion","authors":"Adel Alameh","doi":"arxiv-2406.00055","DOIUrl":"https://doi.org/arxiv-2406.00055","url":null,"abstract":"The motion of rockets is part of the study devoted to the motion of variable\u0000mass systems. Notably those in which the mass leaves permanently the considered\u0000system. Rockets are propelled forward by the reaction force produced by the hot\u0000exhausted gases ejected from their tales in the rearward direction. Thus their\u0000motion should not violate Newton's third principle of the equality of action\u0000and reaction forces during the exhaustion process. Nor should it violate\u0000Newton's second law of motion judged by inertial observers. However a close\u0000examination of the study of the motion of rockets in a major part of physics\u0000textbooks, if not all reveals erroneous determination of the expression of the\u0000thrust force that pushes the rocket in the forward direction. The false\u0000expression of the thrust force entails a bad effect on obtaining the right\u0000differential equation that governs the motion of rockets. This trap induced\u0000some prominent physics authors to pretend the in applicability of Newton's\u0000second law in such particular cases. Not only that, but they also modified\u0000Newton's second law in order to fit their purposes of obtaining the right\u0000differential equation, historically known under the name Tsiolkovsky rocket\u0000equation. The object of this paper is to give the true expression of the thrust\u0000force and to write the differential equation of motion of rockets without any\u0000necessity of modification of the classical laws. The paper also delves into the\u0000expression of the change of velocity of rockets, and proves that their motion\u0000is uniformly accelerated in the early stages of liftoff from the ground at\u0000condition of constant velocity of expulsion of hot gases from their nozzles.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141258852","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 long-term evolution of astrophysical systems is driven by a Hamiltonian that is independent of the fast angle. As this Hamiltonian may contain explicitly time-dependent parameters, the conservation of mechanical energy is not guaranteed in such systems. We derive how the semi-major axis evolves in these cases. We analyze two astrophysically interesting examples, those of the harmonic and quadrupole perturbations.
{"title":"Lagrange's planetary equations with time-dependent secular perturbations","authors":"Barnabás Deme","doi":"arxiv-2405.18140","DOIUrl":"https://doi.org/arxiv-2405.18140","url":null,"abstract":"The long-term evolution of astrophysical systems is driven by a Hamiltonian\u0000that is independent of the fast angle. As this Hamiltonian may contain\u0000explicitly time-dependent parameters, the conservation of mechanical energy is\u0000not guaranteed in such systems. We derive how the semi-major axis evolves in\u0000these cases. We analyze two astrophysically interesting examples, those of the\u0000harmonic and quadrupole perturbations.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141166804","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 simple formula for the gauge function of the transformation from the Lorenz gauge to the Coulomb gauge, valid under a condition that is satisfied by some charge densities employed in the literature, is derived.
{"title":"Note on the transformation from the Lorenz gauge to the Coulomb gauge","authors":"V. Hnizdo","doi":"arxiv-2405.16530","DOIUrl":"https://doi.org/arxiv-2405.16530","url":null,"abstract":"A simple formula for the gauge function of the transformation from the Lorenz\u0000gauge to the Coulomb gauge, valid under a condition that is satisfied by some\u0000charge densities employed in the literature, is derived.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141173414","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 two-thirds power law is a link between angular speed $omega$ and curvature $kappa$ observed in voluntary human movements: $omega$ is proportional to $kappa^{2/3}$. Squared jerk is known to be a Lagrangian leading to the latter law. We propose that a broader class of higher-derivative Lagrangians leads to the two-thirds power law and we perform the Hamiltonian analysis leading to action-angle variables through Ostrogradski's procedure. In this framework, squared jerk appears as an action variable and its minimization may be related to power expenditure minimization during motion. The identified higher-derivative Lagrangians are therefore natural candidates for cost functions, i.e. movement functions that are targeted to be minimal when one individual performs a voluntary movement.
{"title":"The two-thirds power law derived from an higher-derivative action","authors":"N. Boulanger, F. Buisseret, F. Dierick, O. White","doi":"arxiv-2405.15503","DOIUrl":"https://doi.org/arxiv-2405.15503","url":null,"abstract":"The two-thirds power law is a link between angular speed $omega$ and\u0000curvature $kappa$ observed in voluntary human movements: $omega$ is\u0000proportional to $kappa^{2/3}$. Squared jerk is known to be a Lagrangian\u0000leading to the latter law. We propose that a broader class of higher-derivative\u0000Lagrangians leads to the two-thirds power law and we perform the Hamiltonian\u0000analysis leading to action-angle variables through Ostrogradski's procedure. In\u0000this framework, squared jerk appears as an action variable and its minimization\u0000may be related to power expenditure minimization during motion. The identified\u0000higher-derivative Lagrangians are therefore natural candidates for cost\u0000functions, i.e. movement functions that are targeted to be minimal when one\u0000individual performs a voluntary movement.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"223 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141166746","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}
Chenbo Shi, Jin Pan, Xin Gu, Shichen Liang, Le Zuo
This paper presents a novel approach for computing substructure characteristic modes. This method leverages electromagnetic scattering matrices and spherical wave expansion to directly decompose electromagnetic fields. Unlike conventional methods that rely on the impedance matrix generated by the method of moments (MoM), our technique simplifies the problem into a small-scale ordinary eigenvalue problem, improving numerical dynamics and computational efficiency. We have developed analytical substructure characteristic mode solutions for a scenario involving two spheres, which can serve as benchmarks for evaluating other numerical solvers. A key advantage of our method is its independence from specific MoM frameworks, allowing for the use of various numerical methods. This flexibility paves the way for substructure characteristic mode decomposition to become a universal frequency technique.
{"title":"The Scattering Matrix-Based Characteristic Mode for Structure amidst Arbitrary Background: Theory, Benchmark and Applications","authors":"Chenbo Shi, Jin Pan, Xin Gu, Shichen Liang, Le Zuo","doi":"arxiv-2405.15627","DOIUrl":"https://doi.org/arxiv-2405.15627","url":null,"abstract":"This paper presents a novel approach for computing substructure\u0000characteristic modes. This method leverages electromagnetic scattering matrices\u0000and spherical wave expansion to directly decompose electromagnetic fields.\u0000Unlike conventional methods that rely on the impedance matrix generated by the\u0000method of moments (MoM), our technique simplifies the problem into a\u0000small-scale ordinary eigenvalue problem, improving numerical dynamics and\u0000computational efficiency. We have developed analytical substructure\u0000characteristic mode solutions for a scenario involving two spheres, which can\u0000serve as benchmarks for evaluating other numerical solvers. A key advantage of\u0000our method is its independence from specific MoM frameworks, allowing for the\u0000use of various numerical methods. This flexibility paves the way for\u0000substructure characteristic mode decomposition to become a universal frequency\u0000technique.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141166863","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}
We derive the constitutive equation for a suspension of lopsided Hookean dumbbells. By lopsided, we mean that one bead is larger than the other. We find that all results derived for symmetric Hookean dumbbells can be taken over for lopsided ones by replacing$ frac{2}{zeta}$ with $frac{1}{zeta_1}+frac{1}{zeta_2}$, where ${zeta}$, ${zeta}_1$ and ${zeta}_2$ are the bead friction coefficients for the symmetric dumbbell beads, and the first and second beads of the lopsided dumbbell respectively.
{"title":"Lopsided Elastic Dumbbell Suspension","authors":"N. Phan-Thien, M. A. Kanso, A. J. Giacomin","doi":"arxiv-2405.20227","DOIUrl":"https://doi.org/arxiv-2405.20227","url":null,"abstract":"We derive the constitutive equation for a suspension of lopsided Hookean\u0000dumbbells. By lopsided, we mean that one bead is larger than the other. We find\u0000that all results derived for symmetric Hookean dumbbells can be taken over for\u0000lopsided ones by replacing$ frac{2}{zeta}$ with\u0000$frac{1}{zeta_1}+frac{1}{zeta_2}$, where ${zeta}$, ${zeta}_1$ and\u0000${zeta}_2$ are the bead friction coefficients for the symmetric dumbbell\u0000beads, and the first and second beads of the lopsided dumbbell respectively.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"64 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141197188","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}
Wei Wang, Yang Tan, Jingjing Liu, Bin Liang, Jianchun Cheng
Acoustic waves in fluid with spin-0 nature have been long believed not to support spin Hall effect and strong orbital Hall effect that enables experimental observation. Here we report the first theoretical explication and experimental demonstration of giant acoustic geometric spin and orbital Hall effect characterized by a large transverse shift. We reveal that this effect occurs when a vortex beam is observed from a tilted reference frame free of wave-interface interactions or gradient-index media needed for observing conventional ones, and can be amplified by simply binding the beam tightly. Thanks to this mechanism, large transverse shifts proportional to angular momentum are observed in a compact system. Our work provides deeper insights into the physics of angular momentum of classic waves.
{"title":"Giant Acoustic Geometric Spin and Orbital Hall Effect","authors":"Wei Wang, Yang Tan, Jingjing Liu, Bin Liang, Jianchun Cheng","doi":"arxiv-2405.14202","DOIUrl":"https://doi.org/arxiv-2405.14202","url":null,"abstract":"Acoustic waves in fluid with spin-0 nature have been long believed not to\u0000support spin Hall effect and strong orbital Hall effect that enables\u0000experimental observation. Here we report the first theoretical explication and\u0000experimental demonstration of giant acoustic geometric spin and orbital Hall\u0000effect characterized by a large transverse shift. We reveal that this effect\u0000occurs when a vortex beam is observed from a tilted reference frame free of\u0000wave-interface interactions or gradient-index media needed for observing\u0000conventional ones, and can be amplified by simply binding the beam tightly.\u0000Thanks to this mechanism, large transverse shifts proportional to angular\u0000momentum are observed in a compact system. Our work provides deeper insights\u0000into the physics of angular momentum of classic waves.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153768","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}
Nicolas FaresLOMA, Maxime LavaudLOMA, Zaicheng ZhangLOMA, Aditya JhaLOMA, Yacine AmaroucheneLOMA, Thomas SalezLOMA
Confined motions in complex environments are ubiquitous in microbiology. These situations invariably involve the intricate coupling between fluid flow, soft boundaries, surface forces and fluctuations. In the present study, such a coupling is investigated using a novel method combining holographic microscopy and advanced statistical inference. Specifically, the Brownian motion of softmicrometric oil droplets near rigid walls is quantitatively analyzed. All the key statistical observables are reconstructed with high precision, allowing for nanoscale resolution of local mobilities and femtonewton inference of conservative or non-conservative forces. Strikingly, the analysis reveals the existence of a novel, transient, but large, soft Brownian force. The latter might be of crucial importance for microbiological and nanophysical transport, target finding or chemical reactions in crowded environments, and hence the whole life machinery.
{"title":"Observation of Brownian elastohydrodynamic forces acting on confined soft colloids","authors":"Nicolas FaresLOMA, Maxime LavaudLOMA, Zaicheng ZhangLOMA, Aditya JhaLOMA, Yacine AmaroucheneLOMA, Thomas SalezLOMA","doi":"arxiv-2405.13434","DOIUrl":"https://doi.org/arxiv-2405.13434","url":null,"abstract":"Confined motions in complex environments are ubiquitous in microbiology.\u0000These situations invariably involve the intricate coupling between fluid flow,\u0000soft boundaries, surface forces and fluctuations. In the present study, such a\u0000coupling is investigated using a novel method combining holographic microscopy\u0000and advanced statistical inference. Specifically, the Brownian motion of\u0000softmicrometric oil droplets near rigid walls is quantitatively analyzed. All\u0000the key statistical observables are reconstructed with high precision, allowing\u0000for nanoscale resolution of local mobilities and femtonewton inference of\u0000conservative or non-conservative forces. Strikingly, the analysis reveals the\u0000existence of a novel, transient, but large, soft Brownian force. The latter\u0000might be of crucial importance for microbiological and nanophysical transport,\u0000target finding or chemical reactions in crowded environments, and hence the\u0000whole life machinery.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151585","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 rod and slit paradox, as first proposed by R. Shaw, is revisited. In this paradox, a rod of rest length $l_0$ moves parallel to the horizontal x-axis. Simultaneously, a thin sheet parallel to the horizontal xz-plane with a rod-shaped slit of rest length $d < l_0$ moves along the vertical y-axis. The rod passes through the slit due to relativistic effects. Earlier papers do not link the thought experiment to the Silberstein/Thomas/Wigner-rotation (STW-rotation), which is essential to its outcome. In this paper the role of the STW-rotation is discussed, and additional clarifying figures are provided. Some misleading aspects of earlier treatments are pointed out and corrected.
本文重新探讨了由 R. Shaw 首次提出的棒与缝悖论。在这个悖论中，一根静止长度为 $l_0$ 的杆平行于水平 x 轴运动，与此同时，平行于水平 xz 平面的薄片沿着垂直 y 轴运动，薄片上有一个静止长度为 $d < l_0$ 的杆状狭缝。由于相对论效应，杆穿过狭缝。早先的论文没有把思想实验与西尔伯斯坦/托马斯/维格纳旋转（STW-rotation）联系起来，而STW-rotation对思想实验的结果至关重要。本文讨论了 STW 旋转的作用，并提供了更多说明性数字，同时指出并纠正了先前论述中的一些误导之处。
{"title":"The role of the Silberstein/Thomas/Wigner-rotation in the rod and slit paradox","authors":"Mads Vestergaard Schmidt, Erich Schoedl","doi":"arxiv-2405.13040","DOIUrl":"https://doi.org/arxiv-2405.13040","url":null,"abstract":"The rod and slit paradox, as first proposed by R. Shaw, is revisited. In this\u0000paradox, a rod of rest length $l_0$ moves parallel to the horizontal x-axis.\u0000Simultaneously, a thin sheet parallel to the horizontal xz-plane with a\u0000rod-shaped slit of rest length $d < l_0$ moves along the vertical y-axis. The\u0000rod passes through the slit due to relativistic effects. Earlier papers do not\u0000link the thought experiment to the Silberstein/Thomas/Wigner-rotation\u0000(STW-rotation), which is essential to its outcome. In this paper the role of\u0000the STW-rotation is discussed, and additional clarifying figures are provided.\u0000Some misleading aspects of earlier treatments are pointed out and corrected.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151497","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}
Mariia Krasikova, Felix Kronowetter, Mikhail Kuzmin, Sergey Krasikov, Marcus Maeder, Tao Yang, Anton Melnikov, Steffen Marburg, Andrey Bogdanov
Resonant states underlie a variety of metastructures that exhibit remarkable capabilities for effective control of acoustic waves at subwavelength scales. The development of metamaterials relies on the rigorous mode engineering providing the implementation of the desired properties. At the same time, the application of metamaterials is still limited as their building blocks are frequently characterized by complicated geometry and can't be tuned easily. In this work, we consider a simple system of coupled Helmholtz resonators and study their properties associated with the tuning of coupling strength and symmetry breaking. We numerically and experimentally demonstrate the excitation of quasi-bound state in the continuum in the resonators placed in a free space and in a rectangular cavity. It is also shown that tuning the intrinsic losses via introducing porous inserts can lead to spectral splitting or merging of quasi-bound states in the continuum and occurrence of exceptional points. The obtained results will open new opportunities for the development of simple and easy-tunable metastructures based on Helmholtz resonances.
{"title":"Acoustic Bound States in the Continuum and Exceptional Points in Coupled Helmholtz Resonators","authors":"Mariia Krasikova, Felix Kronowetter, Mikhail Kuzmin, Sergey Krasikov, Marcus Maeder, Tao Yang, Anton Melnikov, Steffen Marburg, Andrey Bogdanov","doi":"arxiv-2405.07383","DOIUrl":"https://doi.org/arxiv-2405.07383","url":null,"abstract":"Resonant states underlie a variety of metastructures that exhibit remarkable\u0000capabilities for effective control of acoustic waves at subwavelength scales.\u0000The development of metamaterials relies on the rigorous mode engineering\u0000providing the implementation of the desired properties. At the same time, the\u0000application of metamaterials is still limited as their building blocks are\u0000frequently characterized by complicated geometry and can't be tuned easily. In\u0000this work, we consider a simple system of coupled Helmholtz resonators and\u0000study their properties associated with the tuning of coupling strength and\u0000symmetry breaking. We numerically and experimentally demonstrate the excitation\u0000of quasi-bound state in the continuum in the resonators placed in a free space\u0000and in a rectangular cavity. It is also shown that tuning the intrinsic losses\u0000via introducing porous inserts can lead to spectral splitting or merging of\u0000quasi-bound states in the continuum and occurrence of exceptional points. The\u0000obtained results will open new opportunities for the development of simple and\u0000easy-tunable metastructures based on Helmholtz resonances.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"124 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140942393","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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