1 Classical Theory and Atomistics
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Literature Compass Editing Humphry Davy's
1 ‘Work in Progress in Romanticism’ Literature Compass Editing Humphry Davy’s Letters Tim Fulford, Andrew Lacey, Sharon Ruston An editorial team of Tim Fulford (De Montfort University) and Sharon Ruston (Lancaster University) (co-editors), and Jan Golinski (University of New Hampshire), Frank James (the Royal Institution of Great Britain), and David Knight1 (Durham University) (advisory editors) are currently preparing The Collected Letters of Sir Humphry Davy: a four-volume edition of the c. 1200 surviving letters of Davy (1778-1829) and his immediate circle, for publication with Oxford University Press, in both print and electronic forms, in 2020. Davy was one of the most significant and famous figures in the scientific and literary culture of early nineteenth-century Britain, Europe, and America. Davy’s scientific accomplishments were varied and numerous, including conducting pioneering research into the physiological effects of nitrous oxide (laughing gas); isolating potassium, calcium, and several other metals; inventing a miners’ safety lamp (the bicentenary of which was celebrated in 2015); developing the electrochemical protection of the copper sheeting of Royal Navy vessels; conserving the Herculaneum papyri; writing an influential text on agricultural chemistry; and seeking to improve the quality of optical glass. But Davy’s endeavours were not merely limited to science: he was also a poet, and moved in the same literary circles as Lord Byron, Samuel Taylor Coleridge, Robert Southey, and William Wordsworth. Since his death, Davy has rarely been out of the public mind. He is still the frequent subject of biographies (by, 1 David Knight died in 2018. David gave generously to the Davy Letters Project, and a two-day conference at Durham University was recently held in his memory. -
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 . -
A NONSMOOTH APPROACH for the MODELLING of a MECHANICAL ROTARY DRILLING SYSTEM with FRICTION Samir Adly, Daniel Goeleven
A NONSMOOTH APPROACH FOR THE MODELLING OF A MECHANICAL ROTARY DRILLING SYSTEM WITH FRICTION Samir Adly, Daniel Goeleven To cite this version: Samir Adly, Daniel Goeleven. A NONSMOOTH APPROACH FOR THE MODELLING OF A ME- CHANICAL ROTARY DRILLING SYSTEM WITH FRICTION. Evolution Equations and Control Theory, AIMS, In press, X, 10.3934/xx.xx.xx.xx. hal-02433100 HAL Id: hal-02433100 https://hal.archives-ouvertes.fr/hal-02433100 Submitted on 8 Jan 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Manuscript submitted to doi:10.3934/xx.xx.xx.xx AIMS’ Journals Volume X, Number 0X, XX 200X pp. X–XX A NONSMOOTH APPROACH FOR THE MODELLING OF A MECHANICAL ROTARY DRILLING SYSTEM WITH FRICTION SAMIR ADLY∗ Laboratoire XLIM, Universite´ de Limoges 87060 Limoges, France. DANIEL GOELEVEN Laboratoire PIMENT, Universite´ de La Reunion´ 97400 Saint-Denis, France Dedicated to 70th birthday of Professor Meir Shillor. ABSTRACT. In this paper, we show how the approach of nonsmooth dynamical systems can be used to develop a suitable method for the modelling of a rotary oil drilling system with friction. We study different kinds of frictions and analyse the mathematical properties of the involved dynamical systems. -
Foundations of Newtonian Dynamics: an Axiomatic Approach For
Foundations of Newtonian Dynamics: 1 An Axiomatic Approach for the Thinking Student C. J. Papachristou 2 Department of Physical Sciences, Hellenic Naval Academy, Piraeus 18539, Greece Abstract. Despite its apparent simplicity, Newtonian mechanics contains conceptual subtleties that may cause some confusion to the deep-thinking student. These subtle- ties concern fundamental issues such as, e.g., the number of independent laws needed to formulate the theory, or, the distinction between genuine physical laws and deriva- tive theorems. This article attempts to clarify these issues for the benefit of the stu- dent by revisiting the foundations of Newtonian dynamics and by proposing a rigor- ous axiomatic approach to the subject. This theoretical scheme is built upon two fun- damental postulates, namely, conservation of momentum and superposition property for interactions. Newton’s laws, as well as all familiar theorems of mechanics, are shown to follow from these basic principles. 1. Introduction Teaching introductory mechanics can be a major challenge, especially in a class of students that are not willing to take anything for granted! The problem is that, even some of the most prestigious textbooks on the subject may leave the student with some degree of confusion, which manifests itself in questions like the following: • Is the law of inertia (Newton’s first law) a law of motion (of free bodies) or is it a statement of existence (of inertial reference frames)? • Are the first two of Newton’s laws independent of each other? It appears that -
Conservative Forces and Potential Energy
Program 7 / Chapter 7 Conservative forces and potential energy In the motion of a mass acted on by a conservative force the total energy in the system, which is the sum of the kinetic and potential energies, is conserved. In this section, this motion is computed numerically using the Euler–Cromer method. Theory In section 7–2 of your textbook the oscillatory motion of a mass attached to a spring is described in the context of energy conservation. Specifically, if the spring is initially compressed then the system has spring potential energy. When the mass is free to move, this potential energy is converted into kinetic energy, K = 1/2mv2. The spring then stretches past its equilibrium position, the potential energy increases again until it equals its initial value. This oscillatory motion is illustrated in Fig. 7–7 of your textbook. Consider the more complicated situation in which the force on the particle is given by F(x) = x - 4qx 3 This is a conservative force and the its potential energy is 1 2 4 U(x) = - 2 x + qx (see Fig. 7–10). From the force, we can calculate the motion using Newton’s second law. The program that you will use in this section calculates this motion and demonstrates that the total energy, E = K + U, is conserved (i.e., E remains constant). Given the force, F, on an object (of mass m), its position and velocity may be found by solving the two ordinary differential equations, dv 1 dx = F ; = v dt m dt If we replace the derivatives with their right derivative approximations, we have v(t + Dt) - v(t) 1 x(t + Dt) - x(t) = F(t) ; = v(t) Dt m Dt or v - v 1 x - x f i = F ; f i = v Dt m i Dt i where the subscripts i and f refer to the initial (time t) and final (time t+Dt) values. -
Atomic History Project Background: If You Were Asked to Draw the Structure of an Atom, What Would You Draw?
Atomic History Project Background: If you were asked to draw the structure of an atom, what would you draw? Throughout history, scientists have accepted five major different atomic models. Our perception of the atom has changed from the early Greek model because of clues or evidence that have been gathered through scientific experiments. As more evidence was gathered, old models were discarded or improved upon. Your task is to trace the atomic theory through history. Task: 1. You will create a timeline of the history of the atomic model that includes all of the following components: A. Names of 15 of the 21 scientists listed below B. The year of each scientist’s discovery that relates to the structure of the atom C. 1- 2 sentences describing the importance of the discovery that relates to the structure of the atom Scientists for the timeline: *required to be included • Empedocles • John Dalton* • Ernest Schrodinger • Democritus* • J.J. Thomson* • Marie & Pierre Curie • Aristotle • Robert Millikan • James Chadwick* • Evangelista Torricelli • Ernest • Henri Becquerel • Daniel Bernoulli Rutherford* • Albert Einstein • Joseph Priestly • Niels Bohr* • Max Planck • Antoine Lavoisier* • Louis • Michael Faraday • Joseph Louis Proust DeBroglie* Checklist for the timeline: • Timeline is in chronological order (earliest date to most recent date) • Equal space is devoted to each year (as on a number line) • The eight (8) *starred scientists are included with correct dates of their discoveries • An additional seven (7) scientists of your choice (from -
Conservation of Energy for an Isolated System
POTENTIAL ENERGY Often the work done on a system of two or more objects does not change the kinetic energy of the system but instead it is stored as a new type of energy called POTENTIAL ENERGY. To demonstrate this new type of energy let‟s consider the following situation. Ex. Consider lifting a block of mass „m‟ through a vertical height „h‟ by a force F. M vf=0 h M vi=0 Earth Earth System = Block F m s mg WKnet K0 (since vif v 0) WWWnet F g 0 o WFg W mghcos180 WF mgh 1 System = block + earth F system m s Earth Wnet K K 0 Wnet W F mgh WF mgh Clearly the work done by Fapp is not zero and there is no change in KE of the system. Where has the work gone into? Because recall that positive work means energy transfer into the system. Where did the energy go into? The work done by Fext must show up as an increase in the energy of the system. The work done by Fext ends up stored as POTENTIAL ENERGY (gravitational) in the Earth-Block System. This potential energy has the “potential” to be recovered in the form of kinetic energy if the block is released. 2 Ex. Spring-Mass System system N F’ K M F M F xi xf mg wKnet K0 (Since vi v f 0) w w w w w netF ' N mg F w w w net F s 11 w k22 k s22 i f 11 w w k22 k F s22 f i The work done by Fapp ends up stored as POTENTIAL ENERGY (elastic) in the Spring- Mass System. -
Contact Mechanics in Gears a Computer-Aided Approach for Analyzing Contacts in Spur and Helical Gears Master’S Thesis in Product Development
Two Contact Mechanics in Gears A Computer-Aided Approach for Analyzing Contacts in Spur and Helical Gears Master’s Thesis in Product Development MARCUS SLOGÉN Department of Product and Production Development Division of Product Development CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden, 2013 MASTER’S THESIS IN PRODUCT DEVELOPMENT Contact Mechanics in Gears A Computer-Aided Approach for Analyzing Contacts in Spur and Helical Gears Marcus Slogén Department of Product and Production Development Division of Product Development CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 2013 Contact Mechanics in Gear A Computer-Aided Approach for Analyzing Contacts in Spur and Helical Gears MARCUS SLOGÉN © MARCUS SLOGÉN 2013 Department of Product and Production Development Division of Product Development Chalmers University of Technology SE-412 96 Göteborg Sweden Telephone: + 46 (0)31-772 1000 Cover: The picture on the cover page shows the contact stress distribution over a crowned spur gear tooth. Department of Product and Production Development Göteborg, Sweden 2013 Contact Mechanics in Gears A Computer-Aided Approach for Analyzing Contacts in Spur and Helical Gears Master’s Thesis in Product Development MARCUS SLOGÉN Department of Product and Production Development Division of Product Development Chalmers University of Technology ABSTRACT Computer Aided Engineering, CAE, is becoming more and more vital in today's product development. By using reliable and efficient computer based tools it is possible to replace initial physical testing. This will result in cost savings, but it will also reduce the development time and material waste, since the demand of physical prototypes decreases. This thesis shows how a computer program for analyzing contact mechanics in spur and helical gears has been developed at the request of Vicura AB. -
Leonardo Da Vinci's Contributions to Tribology
© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Published as Wear 360-361 (2016) 51-66 http://dx.doi.org/10.1016/j.wear.2016.04.019 Leonardo da Vinci’s studies of friction Ian M. Hutchings University of Cambridge, Department of Engineering, Institute for Manufacturing, 17 Charles Babbage Road, Cambridge CB3 0FS, UK email: [email protected] Abstract Based on a detailed study of Leonardo da Vinci’s notebooks, this review examines the development of his understanding of the laws of friction and their application. His work on friction originated in studies of the rotational resistance of axles and the mechanics of screw threads. He pursued the topic for more than 20 years, incorporating his empirical knowledge of friction into models for several mechanical systems. Diagrams which have been assumed to represent his experimental apparatus are misleading, but his work was undoubtedly based on experimental measurements and probably largely involved lubricated contacts. Although his work had no influence on the development of the subject over the succeeding centuries, Leonardo da Vinci holds a unique position as a pioneer in tribology. Keywords: sliding friction; rolling friction; history of tribology; Leonardo da Vinci 1. Introduction Although the word ‘tribology’ was first coined almost 450 years after the death of Leonardo da Vinci (1452 – 1519), it is clear that Leonardo was fully familiar with the basic tribological concepts of friction, lubrication and wear. He has been widely credited with the first quantitative investigations of friction, and with the definition of the two fundamental ‘laws’ of friction some two hundred years before they were enunciated (in 1699) by Guillaume Amontons, with whose name they are now usually associated. -
AC Fischer-Cripps
A.C. Fischer-Cripps Introduction to Contact Mechanics Series: Mechanical Engineering Series ▶ Includes a detailed description of indentation stress fields for both elastic and elastic-plastic contact ▶ Discusses practical methods of indentation testing ▶ Supported by the results of indentation experiments under controlled conditions Introduction to Contact Mechanics, Second Edition is a gentle introduction to the mechanics of solid bodies in contact for graduate students, post doctoral individuals, and the beginning researcher. This second edition maintains the introductory character of the first with a focus on materials science as distinct from straight solid mechanics theory. Every chapter has been 2nd ed. 2007, XXII, 226 p. updated to make the book easier to read and more informative. A new chapter on depth sensing indentation has been added, and the contents of the other chapters have been completely overhauled with added figures, formulae and explanations. Printed book Hardcover ▶ 159,99 € | £139.99 | $199.99 The author begins with an introduction to the mechanical properties of materials, ▶ *171,19 € (D) | 175,99 € (A) | CHF 189.00 general fracture mechanics and the fracture of brittle solids. This is followed by a detailed description of indentation stress fields for both elastic and elastic-plastic contact. The discussion then turns to the formation of Hertzian cone cracks in brittle materials, eBook subsurface damage in ductile materials, and the meaning of hardness. The author Available from your bookstore or concludes with an overview of practical methods of indentation. ▶ springer.com/shop MyCopy 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]. -
John Dalton By: Period 8 Early Years and Education
John Dalton By: Period 8 Early Years and Education • John Dalton was born in the small British village of Eaglesfield, Cumberland, England to a Quaker family. • As a child, John did not have much formal education because his family was rather poor; however, he did acquire a basic foundation in reading, writing, and arithmetic at a nearby Quaker school. • A teacher by the name of John Fletcher took young John Dalton under his wing and introduced him to a great mentor, Elihu Robinson, who was a rich Quaker. • Elihu then agreed to tutor John in mathematics, science, and meteorology. Shortly after he ended his tutoring sessions with Elihu, Dalton began keeping a daily log of the weather and other matters of meteorology. Education continued • His studies of these weather conditions led him to develop theories and hypotheses about mixed gases and water vapor. • He kept this journal of weather recordings his entire life, which later aided him in his observations and recordings of atoms and elements. Accomplishments • In 1794, Dalton became the first • Dalton joined the Manchester to explain color blindness, Literary and Philosophical which he was afflicted with Society and instantly published himself, at one of his public his first book on Meteorological lectures and it is even Observations and Essays. sometimes called Daltonism referring to John Dalton • In this book, John tells of his himself. ideas on gasses and that “in a • The first paper he wrote on this mixture of gasses, each gas matter was entitled exists independently of each Extraordinary facts relating to other gas and acts accordingly,” the visions of colors “in which which was when he’s famous he postulated that shortage in ideas on the Atomic Theory color perception was caused by started to form. -
6. Non-Inertial Frames
6. Non-Inertial Frames We stated, long ago, that inertial frames provide the setting for Newtonian mechanics. But what if you, one day, find yourself in a frame that is not inertial? For example, suppose that every 24 hours you happen to spin around an axis which is 2500 miles away. What would you feel? Or what if every year you spin around an axis 36 million miles away? Would that have any e↵ect on your everyday life? In this section we will discuss what Newton’s equations of motion look like in non- inertial frames. Just as there are many ways that an animal can be not a dog, so there are many ways in which a reference frame can be non-inertial. Here we will just consider one type: reference frames that rotate. We’ll start with some basic concepts. 6.1 Rotating Frames Let’s start with the inertial frame S drawn in the figure z=z with coordinate axes x, y and z.Ourgoalistounderstand the motion of particles as seen in a non-inertial frame S0, with axes x , y and z , which is rotating with respect to S. 0 0 0 y y We’ll denote the angle between the x-axis of S and the x0- axis of S as ✓.SinceS is rotating, we clearly have ✓ = ✓(t) x 0 0 θ and ✓˙ =0. 6 x Our first task is to find a way to describe the rotation of Figure 31: the axes. For this, we can use the angular velocity vector ! that we introduced in the last section to describe the motion of particles.