A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account. The quadratic law for the resistance force is used. An analytic approach applies for the investigation. Equations of the projectile motion are solved analytically for an arbitrarily large period of time. The constructed analytical solutions are universal. As a limit case of motion, the vertical asymptote formula is obtained. The value of the vertical asymptote is calculated directly from the initial conditions of motion. There is no need to study the problem numerically. The found analytical solutions are highly accurate over a wide range of parameters. The motion of a baseball, a tennis ball and shuttlecock of badminton are presented as examples.
{"title":"Analytical construction of the projectile motion trajectory in midair","authors":"P. Chudinov, V. Eltyshev, Yuri Barykin","doi":"10.15446/MO.N62.90752","DOIUrl":"https://doi.org/10.15446/MO.N62.90752","url":null,"abstract":"A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account. The quadratic law for the resistance force is used. An analytic approach applies for the investigation. Equations of the projectile motion are solved analytically for an arbitrarily large period of time. The constructed analytical solutions are universal. As a limit case of motion, the vertical asymptote formula is obtained. The value of the vertical asymptote is calculated directly from the initial conditions of motion. There is no need to study the problem numerically. The found analytical solutions are highly accurate over a wide range of parameters. The motion of a baseball, a tennis ball and shuttlecock of badminton are presented as examples.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130294582","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}
Pub Date : 2020-05-18DOI: 10.31349/RevMexFis.66.585
E. Flores-Garduño, S. Mancas, H. Rosu, M. Pérez-Maldonado
We analyze the two-dimensional motion of a rigid body due to a constant torque generated by a force acting on the body parallel to the surface on which the body moves extending an old note of Ferris-Prabhu [Am. J. Phys. 38, 1356-1357 (1970)] and supplementing it with a short discussion of the jerking properties
{"title":"Planar motion with Fresnel integrals as components of the velocity","authors":"E. Flores-Garduño, S. Mancas, H. Rosu, M. Pérez-Maldonado","doi":"10.31349/RevMexFis.66.585","DOIUrl":"https://doi.org/10.31349/RevMexFis.66.585","url":null,"abstract":"We analyze the two-dimensional motion of a rigid body due to a constant torque generated by a force acting on the body parallel to the surface on which the body moves extending an old note of Ferris-Prabhu [Am. J. Phys. 38, 1356-1357 (1970)] and supplementing it with a short discussion of the jerking properties","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131212284","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}
Pub Date : 2020-05-15DOI: 10.12841/wood.1644-3985.259.11
G. Koczan, P. Kozakiewicz
Wood is a fibrous orthotropic material additionally characterized with sign-sensitivity. Thus, determining the universal conditions of its strength constitutes a complex task. In their work, the authors present the anisotropic generalization of the Huber criterion which is closer to Norris's proposal, as opposed to Hill (and Hofmann) and Mises proposal. The obtained criterion incorporates conditions which are additionally imposed on a special case of Tsai-Wu criterion for composite materials.
{"title":"Unified anisotropic strength criterion rank two for fibrous materials like wood","authors":"G. Koczan, P. Kozakiewicz","doi":"10.12841/wood.1644-3985.259.11","DOIUrl":"https://doi.org/10.12841/wood.1644-3985.259.11","url":null,"abstract":"Wood is a fibrous orthotropic material additionally characterized with sign-sensitivity. Thus, determining the universal conditions of its strength constitutes a complex task. In their work, the authors present the anisotropic generalization of the Huber criterion which is closer to Norris's proposal, as opposed to Hill (and Hofmann) and Mises proposal. The obtained criterion incorporates conditions which are additionally imposed on a special case of Tsai-Wu criterion for composite materials.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124153646","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}
FFT-based solvers are increasingly used by many researcher groups interested in modelling the mechanical behavior associated to a heterogeneous microstructure. A development is reported here that concerns the viscoelastic behavior of composite structures generally studied experimentally through Dynamic Mechanical Analysis (DMA). A parallelized computation code developed under complex-valued quantities provides virtual DMA experiments directly in the frequency domain on a heterogenous system described by a voxel grid of mechanical properties. The achieved precision and computation times are very good. An effort has been made to show the application of such virtual DMA tool starting from two examples found in the literature: the modelling of glassy/amorphous systems at a small scale and the modelling of experimental data obtained in temperature sweeping mode by DMA on a particulate composite made of glass beads and a polystyrene matrix, at a larger scale. Both examples show how virtual DMA can contribute to question, analyze, understand relaxation phenomena either on the theoretical or experimental point of view.
{"title":"An FFT-solver used for virtual Dynamic Mechanical Analysis experiments: Application on a glassy/amorphous system and on a particulate composite","authors":"S. Andre, J. Boisse, C. Noûs","doi":"10.46298/JTCAM.6450","DOIUrl":"https://doi.org/10.46298/JTCAM.6450","url":null,"abstract":"FFT-based solvers are increasingly used by many researcher groups interested in modelling the mechanical behavior associated to a heterogeneous microstructure. A development is reported here that concerns the viscoelastic behavior of composite structures generally studied experimentally through Dynamic Mechanical Analysis (DMA). A parallelized computation code developed under complex-valued quantities provides virtual DMA experiments directly in the frequency domain on a heterogenous system described by a voxel grid of mechanical properties. The achieved precision and computation times are very good. An effort has been made to show the application of such virtual DMA tool starting from two examples found in the literature: the modelling of glassy/amorphous systems at a small scale and the modelling of experimental data obtained in temperature sweeping mode by DMA on a particulate composite made of glass beads and a polystyrene matrix, at a larger scale. Both examples show how virtual DMA can contribute to question, analyze, understand relaxation phenomena either on the theoretical or experimental point of view.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"351 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115848005","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}
Pub Date : 2020-01-29DOI: 10.22541/au.158316298.89730642
Matt Majić
The electrostatics problem of a point charge next to a conducting plane is best solved by placing an image charge placed on the opposite side. For a charge between two parallel planes this can be solved with image charges outside the planes at evenly spaced intervals moving out to infinity. What is the corresponding image of a point charge is when placed on the axis of a cylinder?. The potential of a point charge in a cylinder is well known and may expressed in many forms involving integrals or series of Bessel functions, but none of which elude to an image. In fact the image is complex (in both senses), consisting of infinitely many rings on a disk with some surface charge distribution. This manuscript attempts to describe the image as accurately as possible, and in doing so finds simple accurate approximations for the potential.
{"title":"The image of a point charge in an infinite conducting cylinder","authors":"Matt Majić","doi":"10.22541/au.158316298.89730642","DOIUrl":"https://doi.org/10.22541/au.158316298.89730642","url":null,"abstract":"The electrostatics problem of a point charge next to a conducting plane is best solved by placing an image charge placed on the opposite side. For a charge between two parallel planes this can be solved with image charges outside the planes at evenly spaced intervals moving out to infinity. What is the corresponding image of a point charge is when placed on the axis of a cylinder?. The potential of a point charge in a cylinder is well known and may expressed in many forms involving integrals or series of Bessel functions, but none of which elude to an image. In fact the image is complex (in both senses), consisting of infinitely many rings on a disk with some surface charge distribution. This manuscript attempts to describe the image as accurately as possible, and in doing so finds simple accurate approximations for the potential.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125032290","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}
Y. Contoyiannis, S. Potirakis, P. Papadopoulos, M. Kampitakis
A device consisted of a set of circular rings, the centers of which lie on an axis, behaves like a solenoid when the ratio of its radius and distance between two successive rings is greater than one. As this ratio decreases, the device deviates a lot from the solenoid behavior.In the same way, a diffraction phenomenon for magnetic field appears when currents of random direction flow through the rings. This phenomenon demonstrates a critical behavior. Thus an extension of diffraction phenomenon can be done beyond the classical wave diffraction. A possible application of this device could be the diffraction of electronic beams.
{"title":"Diffraction-like stratified magnetic field in a device of circular rings","authors":"Y. Contoyiannis, S. Potirakis, P. Papadopoulos, M. Kampitakis","doi":"10.1063/5.0031465","DOIUrl":"https://doi.org/10.1063/5.0031465","url":null,"abstract":"A device consisted of a set of circular rings, the centers of which lie on an axis, behaves like a solenoid when the ratio of its radius and distance between two successive rings is greater than one. As this ratio decreases, the device deviates a lot from the solenoid behavior.In the same way, a diffraction phenomenon for magnetic field appears when currents of random direction flow through the rings. This phenomenon demonstrates a critical behavior. Thus an extension of diffraction phenomenon can be done beyond the classical wave diffraction. A possible application of this device could be the diffraction of electronic beams.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126010045","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 this paper, we show that the linear dielectrics and magnetic materials in matter obey a special kind of mathematical property known as Ces`{a}ro convergence. Then, we also show that the analytical continuation of the linear permittivity & permeability to a complex plane in terms of Riemann zeta function. The metamaterials are fabricated materials with a negative refractive index. These materials, in turn, depend on permittivity & permeability of the linear dielectrics and magnetic materials. Therefore, the Ces`{a}ro convergence property of the linear dielectrics and magnetic materials may be used to fabricate the metamaterials.
{"title":"Metamaterials and Cesàro convergence","authors":"Yuganand Nellambakam, K. S. Shiv Chaitanya","doi":"10.1063/1.5144629","DOIUrl":"https://doi.org/10.1063/1.5144629","url":null,"abstract":"In this paper, we show that the linear dielectrics and magnetic materials in matter obey a special kind of mathematical property known as Ces`{a}ro convergence. Then, we also show that the analytical continuation of the linear permittivity & permeability to a complex plane in terms of Riemann zeta function. The metamaterials are fabricated materials with a negative refractive index. These materials, in turn, depend on permittivity & permeability of the linear dielectrics and magnetic materials. Therefore, the Ces`{a}ro convergence property of the linear dielectrics and magnetic materials may be used to fabricate the metamaterials.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123228481","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}
Helicity plays a unique role as an integral invariant of a dynamical system. In this paper, the concept of helicity in the general setting of Hamiltonian dynamics is discussed. It is shown, through examples, how the conservation of overall helicity can imply a bound on other quantities of the motion in a nontrivial way.
{"title":"Helicity in Hamiltonian dynamical systems.","authors":"M. Glinsky, P. Hjorth","doi":"10.2172/1595915","DOIUrl":"https://doi.org/10.2172/1595915","url":null,"abstract":"Helicity plays a unique role as an integral invariant of a dynamical system. In this paper, the concept of helicity in the general setting of Hamiltonian dynamics is discussed. It is shown, through examples, how the conservation of overall helicity can imply a bound on other quantities of the motion in a nontrivial way.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115172852","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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