Elementary-Mechanics-Using-Python-A-Modern-Course-

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详细说明：Elementary-Mechanics-Using-Python-A-Modern-Course-Combining-Analytical-and-Numerical-Techniques.pdfUndergraduate Lecture Notes in Physics (ULNP) publishes authoritative texts covering topics throughout pure and applied physics. Each title in the series is suitable as a basis for undergraduate instruction, typically containing practice problems, worked examples, chapter summaries,and suggestions for further reading ULNP titles must provide at least one of the following An exceptionally clear and concise treatment of a standard undergraduate subject A solid undergraduate-level introduction to a graduate, advanced, or non-standard subject e A novel perspective or an unusual approach to teachin ubject ULNP especially encourages new, original, and idiosyncratic approaches to physics teaching t the undergraduate level The purpose of ULNP is to provide intriguing, absorbing books that will continue to be the reader's preferred reference throughout their academic career Series editors Neil ashb Professor Emeritus, University of Colorado, Boulder, CO, USA William Brantley Professor, Furman University, Greenville, SC, USA Michael fowler Professor, University of Virginia, Charlottesville, VA, USA Morten Hjorth-Jensen Professor, University of Oslo, Oslo, Norway Michael inglis Professor, SUNY Suffolk County Community College, Long Island, NY, USA Heinz Klose Professor Emeritus, Humboldt University Berlin, Germany Helmy Sherif Professor, University of Alberta, Edmonton, AB, Canada Moreinformationaboutthisseriesathttp://www.springer.com/series/8917 Anders malthe-Sorenssen Elementary Mechanics Using Python A Modern Course combining analytical and numerical Techniques 空 Springer Anders malthe-Sorenssen Department of physics University of Oslo ay ISSN2192-4791 issN 2192-4805 (electronic) Undergraduate Lecture Notes in Physics ISBN978-3-319-19595-7 ISBN978-3-319-19596-4( e Book) DOI10.1007/978-3-319195964 Library of Congress Control Number: 2015940747 Springer Cham Heidelberg New York Dordrecht London C Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media www.springer.com To Mina. aurora and olav Preface This book was developed as a textbook for use in the course "Introduction to Mechanics,in the Department of Physics at the University of oslo starting 2007. In this course we aimed at providing a seamless integration of analytical and numerical methods when solving physics problems, thereby allowing us to solve more advanced and applied problems in mechanics, and providing examples that are perceived as more relevant for the students. We could address not only the very special cases that have analytical solutions, but could instead focus on choosin problems that would initiate discussions and provide the students with physical Insights Through the processes of introducing and developing advanced problems, it also became clear that this approach brought the students closer to the way physics is discovered and applied. In addition, it introduced the students to a more exploratory way of understanding phenomena and of developing their physical concepts. Well- developed examples that also include elements of numerical computations gave the students a feeling of discovering physical processes while also understanding how they are results of the underlying simple physical laws. In many cases, the advanced examples and exercises spawned interesting and rewarding discussions about the underlying physical processes, and also forced the students to understand the various forms of representation used to illustrate physical processes, such as motion diagrams and energy diagrams, and use these diagrams to reason about physical processes. As the course, examples, and exercises were developed it also became clear that the introduction of numerical methods in an introductory course in physics also helped build the notion that numerical methods are no different from analytical methods -they are part of the theoretical toolbox that any physicist is supposed to master. Our aim became to make it as natural for our students to solve their problems by developing a small program and discussing the results, as it was to use a calculator It has been particularly rewarding to observe the way that many of the examples and exercises trigger discussions when students discover unexpected results, in the form of unexpected resonances in a simple model for friction or in the case of Preface Greenwood gaps in the distribution of asteroids in the solar system. The insight that the simple laws of mechanics that they learned actually had observable conse quences and explanatory power was often an important insight as well as an important reinforcer for the students. We also believe that this helps the student build a more realistic image of how science actually is done In order to get most of the numerical parts of this text it is advantageous for the students to have some prior knowledge of scientific programming, preferably with a scripting type language such as Matlab or Python, but this is not absolutely nec essary. We encourage readers who are not familiar with scripting type programming first to study Chap. 2. However, in our experience students who read the book, the examples, and do the exercises will already be developing programmers by the end of the course This book grew out of a larger, collaborative effort at the University of oslo I would like to thank morten Hjorth-Jensen and Arnt Inge Vistnes for including me in the physics part of the Computers in Science Education program. I also thank Hans Petter Langtangen and Knut Morken at the Department of Informatics for their dedication, support, and inspiration for introducing numerical approaches in the basic curriculum. i thank the Faculty for Mathematics and Natural Sciences for their support used to develop exercises and examples used in this text I would also like to thank Arnt Inge Vistnes, Jonas van den Brinck, and Sigve Boe Skattum for developing some of the exercises that have been included in this book as examples or exercises. Sigve Boe Skattum has also provided many of the illustrations Oslo Anders malthe-Sorenssen March 2015 Contents Introduction 1.1 Physics 1.2 Mechanics Integrating Numerical Methods 1. 4 Problems and exercises 1.5 How to Learn Physics 1.5.1 Advice for how to Succeed 1. 6 How to Use This book 1123456799 2 Getting Started with Programming 2.1 A Python Calculator 2.2 Scripts and Functions 2. 3 Plotting Data-S 13 2.4 Plotting a Function 15 2.5 Random numbers 19 2.6 Conditions 20 2.7 Reading Real Data 22 2.7.1 Example: Plot of Function and Derivative 22 3 Units and measurement 3.1 Standardized Units 3.2 Changing Units 34 3.3 Uncertainty and Significant Digits 35 3.4 Numerical Representation 36 4 Motion in one dimension 4.1 Description of me 4.1.1 Example: Motion of a falling Tennis ba∥· 43 51 4.2 Calculation of motion 57 4.2.1 Example: Modeling the Motion of a Falling Tennis ball Contents 5 Forces in One dimension 83 5.1 What Is a force? 83 5.2 Identifying Forces 86 5.3 Newton's Second law of motion 88 5.3.1 Example: Acceleration and Forces on a Lunar lander 5.4 Force Models 5.5 Force Model Gravitational force 5.6 Force Model: Viscous force 96 5.6.1 Example: Falling Raindrops 99 5.7. 1 Example: Motion of a Hanging Block 5.7 Force Model: Spring Force 112 5.8 Newton’ s First lay .120 5.9 Newton's Third law 121 5.9.1 Example: Weight in an Elevator 124 6 Motion in two and Three dimensions 139 6.1 Vectors 139 6.2 Description of motion 146 6. 2. 1 Example: Mars Express 153 6.3 Calculation of motion 160 6.3. 1 Example: Feather in the wind 168 6.4 Frames of Reference 6.4.1 Example: Motion of a Boat on a Flowing River 172 7 Forces in two and three dimensions 183 7. 1 Identifying Forces 183 7.2 Newton's Second law 187 7.3 Force Model--Constant Gravity 7.3.1 Example: Motion of a ball with gravity 190 7. 4 Force model-Viscous force 192 7.4.1 Example: Path Through a Tornado 7.5 Force Model--Spring Force 197 7.5.1 Example: Motion of a Bouncing Ball with Air resistance 7. 6 Force Model- -Central Force .205 7.6.1 Example: Comet Trajectory 205 8 Constrained Motion 8.1 Linear motion 215 8.2 Curved motion 217 8.2.1 Example: Acceleration of a Matchbox Car 221 8.2.2 Example: Acceleration of a Rotating rod 222 8.2.3 Example: Normal acceleration in Circular Motion 223

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