Courses for Physics and Astronomy 1
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Classical Mechanics
Classical Mechanics Hyoungsoon Choi Spring, 2014 Contents 1 Introduction4 1.1 Kinematics and Kinetics . .5 1.2 Kinematics: Watching Wallace and Gromit ............6 1.3 Inertia and Inertial Frame . .8 2 Newton's Laws of Motion 10 2.1 The First Law: The Law of Inertia . 10 2.2 The Second Law: The Equation of Motion . 11 2.3 The Third Law: The Law of Action and Reaction . 12 3 Laws of Conservation 14 3.1 Conservation of Momentum . 14 3.2 Conservation of Angular Momentum . 15 3.3 Conservation of Energy . 17 3.3.1 Kinetic energy . 17 3.3.2 Potential energy . 18 3.3.3 Mechanical energy conservation . 19 4 Solving Equation of Motions 20 4.1 Force-Free Motion . 21 4.2 Constant Force Motion . 22 4.2.1 Constant force motion in one dimension . 22 4.2.2 Constant force motion in two dimensions . 23 4.3 Varying Force Motion . 25 4.3.1 Drag force . 25 4.3.2 Harmonic oscillator . 29 5 Lagrangian Mechanics 30 5.1 Configuration Space . 30 5.2 Lagrangian Equations of Motion . 32 5.3 Generalized Coordinates . 34 5.4 Lagrangian Mechanics . 36 5.5 D'Alembert's Principle . 37 5.6 Conjugate Variables . 39 1 CONTENTS 2 6 Hamiltonian Mechanics 40 6.1 Legendre Transformation: From Lagrangian to Hamiltonian . 40 6.2 Hamilton's Equations . 41 6.3 Configuration Space and Phase Space . 43 6.4 Hamiltonian and Energy . 45 7 Central Force Motion 47 7.1 Conservation Laws in Central Force Field . 47 7.2 The Path Equation . -
Department of Physics and Astronomy 1
Department of Physics and Astronomy 1 PHSX 216 and PHSX 236, provide a calculus-based foundation in Department of Physics physics for students in physical science, engineering, and mathematics. PHSX 313 and the laboratory course, PHSX 316, provide an introduction and Astronomy to modern physics for majors in physics and some engineering and physical science programs. Why study physics and astronomy? Students in biological sciences, health sciences, physical sciences, mathematics, engineering, and prospective elementary and secondary Our goal is to understand the physical universe. The questions teachers should see appropriate sections of this catalog and major addressed by our department’s research and education missions range advisors for guidance about required physics course work. Chemistry from the applied, such as an improved understanding of the materials that majors should note that PHSX 211 and PHSX 212 are prerequisites to can be used for solar cell energy production, to foundational questions advanced work in chemistry. about the nature of mass and space and how the Universe was formed and subsequently evolved, and how astrophysical phenomena affected For programs in engineering physics (http://catalog.ku.edu/engineering/ the Earth and its evolution. We study the properties of systems ranging engineering-physics/), see the School of Engineering section of the online in size from smaller than an atom to larger than a galaxy on timescales catalog. ranging from billionths of a second to the age of the universe. Our courses and laboratory/research experiences help students hone their Graduate Programs problem solving and analytical skills and thereby become broadly trained critical thinkers. While about half of our majors move on to graduate The department offers two primary graduate programs: (i) an M.S. -
Inspec Archive - List of Journals Covered Between 1898 and 1968
February 2006 www.iee.org/inspec Inspec Archive - List of Journals Covered between 1898 and 1968 Abhandlungen der Berlin Akademie Acta Universitatis Lundensis. Sectio II. Medica, Abhandlungen der Braunschweigischen Mathematica, Scientiae Rerum Naturalium Wissenschaftlichen Gesellschaft Acta Universitatis Tamperensis Abhandlungen der Deutschen Akademie der Acustica Wissenschaften zu Berlin, Klasse fur Advanced Energy Conversion Mathematik, Physik und Technik Advances in Atomic and Molecular Physics Abhandlungen der Konigliches Preussisches Advances in Electronics Meteorologies Institut Advances in Physics Abhandlungen der Preussischen Akademieder Advances in Theoretical Physics Wissenschaften Advances of Science Accademia delle Scienze, Medico e Naturali, AEG Mitteilungen Ferrara AEG Progress ACEC Journal AEG Zeitung ACEC Review AEI Engineering Acero y Energia AEI Engineering Review Acta Academiae Aboensis, Mathematical AEI Journal of Telecommunications Physics AEI Research Laboratory Reports Acta and Commentationes Universitatis Aerial Age Tartuensis (Dorpatensis) Aerial Age Weekly Acta Automatica Sinica Aeronautical Engineering Review Acta Bolyaiana Aeronautical Journal Acta Chemica Scandinavica Aeronautical Research Council Current Papers Acta Crystallographica Aeronautical Research Council Reports and Acta Electronica Memoranda Acta Electronica Sinica Aeronautics Acta Geophysica Sinica Aeroplane Acta Mathematica Aerospace Engineering Acta Mathematica Sinica Agricultural and Horticultural Engineering Acta Mechanica Abstracts Acta Medica -
The Development of the Action Principle a Didactic History from Euler-Lagrange to Schwinger Series: Springerbriefs in Physics
springer.com Walter Dittrich The Development of the Action Principle A Didactic History from Euler-Lagrange to Schwinger Series: SpringerBriefs in Physics Provides a philosophical interpretation of the development of physics Contains many worked examples Shows the path of the action principle - from Euler's first contributions to present topics This book describes the historical development of the principle of stationary action from the 17th to the 20th centuries. Reference is made to the most important contributors to this topic, in particular Bernoullis, Leibniz, Euler, Lagrange and Laplace. The leading theme is how the action principle is applied to problems in classical physics such as hydrodynamics, electrodynamics and gravity, extending also to the modern formulation of quantum mechanics 1st ed. 2021, XV, 135 p. 23 illus., 1 illus. and quantum field theory, especially quantum electrodynamics. A critical analysis of operator in color. versus c-number field theory is given. The book contains many worked examples. In particular, the term "vacuum" is scrutinized. The book is aimed primarily at actively working researchers, Printed book graduate students and historians interested in the philosophical interpretation and evolution of Softcover physics; in particular, in understanding the action principle and its application to a wide range 54,99 € | £49.99 | $69.99 of natural phenomena. [1]58,84 € (D) | 60,49 € (A) | CHF 65,00 eBook 46,00 € | £39.99 | $54.99 [2]46,00 € (D) | 46,00 € (A) | CHF 52,00 Available from your library or springer.com/shop MyCopy [3] Printed eBook for just € | $ 24.99 springer.com/mycopy Order online at springer.com / or for the Americas call (toll free) 1-800-SPRINGER / or email us at: [email protected]. -
Appendix E Nobel Prizes in Nuclear Science
Nuclear Science—A Guide to the Nuclear Science Wall Chart ©2018 Contemporary Physics Education Project (CPEP) Appendix E Nobel Prizes in Nuclear Science Many Nobel Prizes have been awarded for nuclear research and instrumentation. The field has spun off: particle physics, nuclear astrophysics, nuclear power reactors, nuclear medicine, and nuclear weapons. Understanding how the nucleus works and applying that knowledge to technology has been one of the most significant accomplishments of twentieth century scientific research. Each prize was awarded for physics unless otherwise noted. Name(s) Discovery Year Henri Becquerel, Pierre Discovered spontaneous radioactivity 1903 Curie, and Marie Curie Ernest Rutherford Work on the disintegration of the elements and 1908 chemistry of radioactive elements (chem) Marie Curie Discovery of radium and polonium 1911 (chem) Frederick Soddy Work on chemistry of radioactive substances 1921 including the origin and nature of radioactive (chem) isotopes Francis Aston Discovery of isotopes in many non-radioactive 1922 elements, also enunciated the whole-number rule of (chem) atomic masses Charles Wilson Development of the cloud chamber for detecting 1927 charged particles Harold Urey Discovery of heavy hydrogen (deuterium) 1934 (chem) Frederic Joliot and Synthesis of several new radioactive elements 1935 Irene Joliot-Curie (chem) James Chadwick Discovery of the neutron 1935 Carl David Anderson Discovery of the positron 1936 Enrico Fermi New radioactive elements produced by neutron 1938 irradiation Ernest Lawrence -
Some Insights from Total Collapse
Some insights from total collapse S´ergio B. Volchan Abstract We discuss the Sundman-Weierstrass theorem of total collapse in its histor- ical context. This remarkable and relatively simple result, a type of stability criterion, is at the crossroads of some interesting developments in the gravi- tational Newtonian N-body problem. We use it as motivation to explore the connections to such important concepts as integrability, singularities and typ- icality in order to gain some insight on the transition from a predominantly quantitative to a novel qualitative approach to dynamical problems that took place at the end of the 19th century. Keywords: Celestial Mechanics; N-body problem; total collapse, singularities. I Introduction Celestial mechanics is one of the treasures of physics. With a rich and fascinating history, 1 it had a pivotal role in the very creation of modern science. After all, it was Hooke’s question on the two-body problem and Halley’s encouragement (and financial resources) that eventually led Newton to publish the Principia, a water- shed. 2 Conversely, celestial mechanics was the testing ground par excellence for the new mechanics, and its triumphs in explaining a wealth of phenomena were decisive in the acceptance of the Newtonian synthesis and the “clockwork universe”. arXiv:0803.2258v1 [physics.hist-ph] 14 Mar 2008 From the beginning, special attention was paid to the N-body problem, the study of the motion of N massive bodies under mutual gravitational forces, taken as a reliable model of the the solar system. The list of scientists that worked on it, starting with Newton himself, makes a veritable hall of fame of mathematics and physics; also, a host of concepts and methods were created which are now part of the vast heritage of modern mathematical-physics: the calculus, complex variables, the theory of errors and statistics, differential equations, perturbation theory, potential theory, numerical methods, analytical mechanics, just to cite a few. -
The Phase Space Elementary Cell in Classical and Generalized Statistics
Entropy 2013, 15, 4319-4333; doi:10.3390/e15104319 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article The Phase Space Elementary Cell in Classical and Generalized Statistics Piero Quarati 1;2;* and Marcello Lissia 2 1 DISAT, Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino I-10129, Italy 2 Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, Monserrato I-09042, Italy; E-Mail: [email protected] * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +39-0706754899; Fax: +39-070510212. Received: 05 September 2013; in revised form: 25 September 2013/ Accepted: 27 September 2013 / Published: 15 October 2013 Abstract: In the past, the phase-space elementary cell of a non-quantized system was set equal to the third power of the Planck constant; in fact, it is not a necessary assumption. We discuss how the phase space volume, the number of states and the elementary-cell volume of a system of non-interacting N particles, changes when an interaction is switched on and the system becomes or evolves to a system of correlated non-Boltzmann particles and derives the appropriate expressions. Even if we assume that nowadays the volume of the elementary cell is equal to the cube of the Planck constant, h3, at least for quantum systems, we show that there is a correspondence between different values of h in the past, with important and, in principle, measurable cosmological and astrophysical consequences, and systems with an effective smaller (or even larger) phase-space volume described by non-extensive generalized statistics. -
A Re-Interpretation of the Concept of Mass and of the Relativistic Mass-Energy Relation
A re-interpretation of the concept of mass and of the relativistic mass-energy relation 1 Stefano Re Fiorentin Summary . For over a century the definitions of mass and derivations of its relation with energy continue to be elaborated, demonstrating that the concept of mass is still not satisfactorily understood. The aim of this study is to show that, starting from the properties of Minkowski spacetime and from the principle of least action, energy expresses the property of inertia of a body. This implies that inertial mass can only be the object of a definition – the so called mass-energy relation - aimed at measuring energy in different units, more suitable to describe the huge amount of it enclosed in what we call the “rest-energy” of a body. Likewise, the concept of gravitational mass becomes unnecessary, being replaceable by energy, thus making the weak equivalence principle intrinsically verified. In dealing with mass, a new unit of measurement is foretold for it, which relies on the de Broglie frequency of atoms, the value of which can today be measured with an accuracy of a few parts in 10 9. Keywords Classical Force Fields; Special Relativity; Classical General Relativity; Units and Standards 1. Introduction Albert Einstein in the conclusions of his 1905 paper “Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?” (“Does the inertia of a body depend upon its energy content? ”) [1] says “The mass of a body is a measure of its energy-content ”. Despite of some claims that the reasoning that brought Einstein to the mass-energy relation was somehow approximated or even defective (starting from Max Planck in 1907 [2], to Herbert E. -
Non-Equilibrium Continuum Physics
Non-Equilibrium Continuum Physics Lecture notes by Eran Bouchbinder (Dated: June 10, 2019) Abstract This course is intended to introduce graduate students to the essentials of modern continuum physics, with a focus on non-equilibrium solid mechanics and within a thermodynamic perspective. Emphasis will be given to general concepts and principles, such as conservation laws, symmetries, material frame-indifference, thermodynamics, dissipation inequalities and non-equilibrium behaviors, stability criteria and configurational forces. Examples will cover a wide range of physical phenomena and applications in diverse disciplines. The power of field theory as a mathematical structure that does not make direct reference to microscopic length scales well below those of the phenomenon of interest will be highlighted. Some basic mathematical tools and methods will be introduced. The course will be self-contained and will highlight essential ideas and basic physical intuition. Together with courses on fluid mechanics and soft condensed matter, a broad background and understanding of continuum physics will be established. The course will be given within a framework of 12-13 two-hour lectures and 12-13 two-hour tutorial sessions with a focus on problem-solving. No prior knowledge of the subject is assumed. Basic knowledge of statistical thermodynamics, vector calculus, differential equations and complex analysis is required. These extended lecture notes are self-contained and in principle no textbook will be followed. Some general references (mainly for the first half of the course), can be found below. 1 Contents I. Introduction: Background and motivation 4 II. Mathematical preliminaries: Tensor Analysis 7 III. Motion, deformation and stress 13 A. -
Report from Trieste: ICTP on the March Why Have More Than 22 000 Scientists Studied at the International Centre for Theoretical Physics? by Akhtar Mahmud Faruqui
Special reports Report from Trieste: ICTP on the march Why have more than 22 000 scientists studied at the International Centre for Theoretical Physics? by Akhtar Mahmud Faruqui A small Roman town under the Caesars, an indepen- responsibility to continue this flow of benefits to society dent municipality in the Middle Ages, a flourishing and, most important, to extend them to the very large international port and trading centre between the West fraction of the world's burgeoning populations that have and East after 1700, and an Italian entity since 1918, thus far — for whatever reason — been denied them," Trieste is a city of entrancing scenic attractions. Tucked D. Allan Bromley has noted.* The report, Physics in away in the northeast of Italy on the Adriatic Sea, the Perspective, strengthens Saiam and Bromley's view: city stands on tree-dotted hills resembling a sunlit sea- "Science is knowing. What man knows about inanimate washed amphitheatre, with the surrounding Carso nature is physics, or rather the most lasting and univer- plateau rated as one of the most enchanting landscapes sal things that he knows make up physics. As he gains in Europe. more knowledge, what would have appeared compli- But Trieste is now known not just for its scenic splen- cated or capricious can be seen as essentially simple and dours or past grandeurs. It is identified increasingly as in a deep sense orderly. And, to understand how things a meeting place of bright scientific minds from the West work is to see how, within environmental constraints and the East, from the North and the South. -
Rethinking 'Classical Physics'
This is a repository copy of Rethinking 'Classical Physics'. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/95198/ Version: Accepted Version Book Section: Gooday, G and Mitchell, D (2013) Rethinking 'Classical Physics'. In: Buchwald, JZ and Fox, R, (eds.) Oxford Handbook of the History of Physics. Oxford University Press , Oxford, UK; New York, NY, USA , pp. 721-764. ISBN 9780199696253 © Oxford University Press 2013. This is an author produced version of a chapter published in The Oxford Handbook of the History of Physics. Reproduced by permission of Oxford University Press. Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ 1 Rethinking ‘Classical Physics’ Graeme Gooday (Leeds) & Daniel Mitchell (Hong Kong) Chapter for Robert Fox & Jed Buchwald, editors Oxford Handbook of the History of Physics (Oxford University Press, in preparation) What is ‘classical physics’? Physicists have typically treated it as a useful and unproblematic category to characterize their discipline from Newton until the advent of ‘modern physics’ in the early twentieth century. -
Applications of Classical Physics
i APPLICATIONS OF CLASSICAL PHYSICS Roger D. Blandford and Kip S. Thorne version 1200.1.K.pdf, January 28, 2013 Preface Please send comments, suggestions, and errata via email to [email protected], or on paper to Kip Thorne, 350-17 Caltech, Pasadena CA 91125 This book is an introduction to the fundamentals and 21st-century applications of all the major branches of classical physics except classical mechanics, electromagnetic theory, and elementary thermodynamics (which we assume the reader has already learned elsewhere). Classical physics and this book deal with physical phenomena on macroscopic scales: scales where the particulate natures of matter and radiation are secondary to the behavior of particles in bulk; scales where particles’ statistical as opposed to individual properties are important, and where matter’s inherent graininess can be smoothed over. In this book, we shall take a journey through spacetime and phase space, through statistical and continuum mechanics (including solids, fluids, and plasmas), and through optics and relativity, both special and general. In our journey, we shall seek to comprehend the fundamental laws of classical physics in their own terms, and also in relation to quantum physics. Using carefully chosen examples, we shall show how the classical laws are applied to important, contemporary, 21st-century problems and to everyday phenomena, and we shall uncover some deep connections among the various fundamental laws, and connections among the practical techniques that are used in different subfields of physics. Many of the most important recent developments in physics—and more generally in science and engineering—involve classical subjects such as optics, fluids, plasmas, random processes, and curved spacetime.