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Lagrange points and regionally conserved quantities 拉格朗日点和区域守恒量
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2024-06-01 DOI: 10.1119/5.0160904
Eric M. Edlund
{"title":"Lagrange points and regionally conserved quantities","authors":"Eric M. Edlund","doi":"10.1119/5.0160904","DOIUrl":"https://doi.org/10.1119/5.0160904","url":null,"abstract":"Lagrange points are the equilibrium points within a restricted three-body system, epitomized by the Trojan asteroids near the L4 and L5 points of the Sun–Jupiter system. They also play a crucial role in some space missions, including the James Webb Space Telescope which is located at the Sun–Earth L2 point. While the existence of five Lagrange points is a well-known feature of the restricted three-body problem, the equations describing the precise location of all five points are not extensively documented. This work presents a derivation of all Lagrange points using polar coordinates and a new normalization scheme that offers a simpler interpretation of solutions compared to prior analyses. A subtle issue concerning the treatment of angular momentum in the potential formulation of this problem is addressed and resolved. The supplementary material to this work contains additional mathematical details and discussion.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141230161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Bell's dynamical route to special relativity 关于贝尔的狭义相对论动力学路径
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2024-06-01 DOI: 10.1119/5.0159408
Frederick W. Strauch
{"title":"On Bell's dynamical route to special relativity","authors":"Frederick W. Strauch","doi":"10.1119/5.0159408","DOIUrl":"https://doi.org/10.1119/5.0159408","url":null,"abstract":"This paper develops the approach to special relativity put forward by John S. Bell. The classical dynamics of an electron orbiting a nucleus in uniform motion is solved analytically and compared to numerical simulations for an accelerated nucleus. The relativistic phenomena of length contraction and time dilation are shown to result from the electric and magnetic forces on the electron when its motion is analyzed in a single frame of reference. The relevance of these results for understanding the theory of special relativity is discussed.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141233589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the state principle of classical thermodynamics 关于经典热力学的状态原理
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2024-06-01 DOI: 10.1119/5.0179939
J. G. Smith, B. E. Schmidt
{"title":"On the state principle of classical thermodynamics","authors":"J. G. Smith, B. E. Schmidt","doi":"10.1119/5.0179939","DOIUrl":"https://doi.org/10.1119/5.0179939","url":null,"abstract":"We discuss the state principle of classical thermodynamics, namely that the thermodynamic state of a simple compressible system can be uniquely determined by specifying two independent properties. We show that for certain combinations of properties, one is not guaranteed to arrive at a unique state. This caveat to the state principle is illustrated with three examples, two involving liquid water and a third using real gases. Finally, we show that to guarantee a unique state for a simple compressible system, the required two independent properties must be chosen from the trio consisting of a thermodynamic potential and its two natural variables.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141232334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum versus classical quenches and the broadening of wave packets 量子淬火与经典淬火以及波包拓宽
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2024-06-01 DOI: 10.1119/5.0174441
K. Schönhammer
{"title":"Quantum versus classical quenches and the broadening of wave packets","authors":"K. Schönhammer","doi":"10.1119/5.0174441","DOIUrl":"https://doi.org/10.1119/5.0174441","url":null,"abstract":"The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed, but a comparison with results for the dynamics in the framework of classical statistical mechanics is useful. Analytical results are presented when the initial and final potentials are harmonic oscillators. When the final potential vanishes, the problem reduces to the broadening of wave packets. A simple introduction to the concept of the Wigner function is presented, which allows a better understanding of the dynamics of general wave packets. It is pointed out how special the broadening of Gaussian wave packets is, the only example usually presented in quantum mechanics textbooks.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141233331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Orbital mechanics with the Global Positioning System 使用全球定位系统的轨道力学
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2024-06-01 DOI: 10.1119/5.0146547
William H. Baird, Kelly R. Patton
{"title":"Orbital mechanics with the Global Positioning System","authors":"William H. Baird, Kelly R. Patton","doi":"10.1119/5.0146547","DOIUrl":"https://doi.org/10.1119/5.0146547","url":null,"abstract":"The recent availability of relatively inexpensive dual-frequency receivers for signals from Global Navigation Satellite Systems (GNSS) provides access to ultra-precise, real-time data such as positions and velocities of dozens of satellites orbiting the Earth. We discuss how these data can be obtained, processed, and analyzed either with or without the actual purchase of a GNSS receiver. The positional information can be used to verify Kepler's three laws at lowest order as well as to reveal the presence of higher-order perturbations such as the oblateness of the Earth and the gravitational influences of the Sun and Moon on these satellites. The supplementary material includes both introductory laboratory exercises and Python scripts used to gather and process data suitable for intermediate courses.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141231767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mutual inductance between an infinite solenoid and a surrounding loop—A paradox resolved 无限螺线管与周围回路之间的互感--悖论的破解
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2024-06-01 DOI: 10.1119/5.0172133
Ian C Malcolm
{"title":"Mutual inductance between an infinite solenoid and a surrounding loop—A paradox resolved","authors":"Ian C Malcolm","doi":"10.1119/5.0172133","DOIUrl":"https://doi.org/10.1119/5.0172133","url":null,"abstract":"Students may calculate the mutual inductance between an infinite solenoid and a surrounding circular loop using an incorrect method that yields the correct answer, causing frustration and confusion. A physical explanation for the agreement of the two methods is provided that is based on the translational symmetry of the solenoid. As a consequence, the conclusion generalizes to infinite uniform solenoids of arbitrary cross section.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141235369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the “contact” hyperfine interaction 关于 "接触 "超精细相互作用
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2024-06-01 DOI: 10.1119/5.0174056
W. Saslow
{"title":"On the “contact” hyperfine interaction","authors":"W. Saslow","doi":"10.1119/5.0174056","DOIUrl":"https://doi.org/10.1119/5.0174056","url":null,"abstract":"When Enrico Fermi analyzed the magnetic interaction between the electron and Na, Cs, and Rb nuclei in 1930, he used the Dirac equation to compute the energy of an electron interacting with a point charge and magnetic dipole (the nucleus) fixed at the origin. After the mathematical dust had settled, he found an interaction that appeared to act only at a single point: the center of the electron wavefunction; it has been called a contact interaction. In 1936, Casimir analyzed the magnetic interaction of proton and neutron spins in the ground state of the deuteron using the Schrödinger equation and classical electrodynamics. Using symmetries appropriate only to s states, and performing an integration by parts, he found that they, too, seemed to interact only at a single common point of the proton and neutron: their center-of-mass. When applied to hydrogen, his result agreed with Fermi's. We present an expanded version of Casimir's important but little-known calculation.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141232587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Linewidth measurement of external cavity lasers 外腔激光器的线宽测量
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2024-06-01 DOI: 10.1119/5.0207084
Tom A. Kuusela
{"title":"Linewidth measurement of external cavity lasers","authors":"Tom A. Kuusela","doi":"10.1119/5.0207084","DOIUrl":"https://doi.org/10.1119/5.0207084","url":null,"abstract":"Narrowband laser sources are used in applications that require high-precision or stable optical frequency. Such applications include high-resolution spectroscopy, long-distance measurement, and coherent optical communication. The linewidth of a laser is a direct measure of the laser's stability; therefore, characterization of laser linewidth is essential. In practice, however, determining a laser's linewidth is not a trivial task and typically requires expensive equipment or a complex experimental arrangement. This paper presents a straightforward, low-cost method based on unbalanced interferometry, which allows us to determine the visibility of fringe patterns as a function of the optical path difference and, consequently, the linewidth of the laser. As a test laser, we use a tunable external cavity laser source at around 780 nm, where an interference filter is employed for wavelength selection. Data obtained by applying the interferometric technique to this laser and the analysis of these data, along with the resulting linewidth value, are presented. Given that the described measurement setup is inexpensive, straightforward, and pedagogically accessible, it is well-suited for an instructional physics laboratory experiment and will also be of interest to laboratory researchers.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141230208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
In this issue: June 2024 本期内容2024 年 6 月
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2024-06-01 DOI: 10.1119/5.0216283
J. Essick, Jesse Kinder, C. Marrache-Kikuchi, Raina Olsen, B. Parks, B. C. Reed, Donald Salisbury, Todd Springer, Keith Zengel
{"title":"In this issue: June 2024","authors":"J. Essick, Jesse Kinder, C. Marrache-Kikuchi, Raina Olsen, B. Parks, B. C. Reed, Donald Salisbury, Todd Springer, Keith Zengel","doi":"10.1119/5.0216283","DOIUrl":"https://doi.org/10.1119/5.0216283","url":null,"abstract":"","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141231127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamics of a bouncing capsule: An impulse model vs a Hertzian model 弹跳胶囊的动力学：脉冲模型与赫兹模型的对比
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2024-06-01 DOI: 10.1119/5.0169258
Xinrui Li, Guangyuan Chen, Ren Jie Tee, Jie Xu Liu, Christopher Ong
{"title":"Dynamics of a bouncing capsule: An impulse model vs a Hertzian model","authors":"Xinrui Li, Guangyuan Chen, Ren Jie Tee, Jie Xu Liu, Christopher Ong","doi":"10.1119/5.0169258","DOIUrl":"https://doi.org/10.1119/5.0169258","url":null,"abstract":"A capsule-shaped object, unlike a sphere, can rebound to a higher height than it is dropped from if it has an initial spin. In this paper, we compare two quantitative models of this phenomenon: an impulse-based analytic model and a force-based Hertzian model. We experimentally studied the effects of impact angular velocity and contact angle on the capsule's rebounding velocity and angular velocity. Our experimental findings showed successful agreement with our Hertzian model but not with our impulse model. We attribute the comparative success of the Hertzian model to its intricate treatment of the slip–stick behavior of friction during the collision.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141230162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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