The Double Pendulum
In preparation of the numerical treatment of the double pendulum, a well known problem of mechanics, Hamilton ’s equations of motion are derived in detail. The problem is then formulated as an initial value problem and the system of ordinary differential
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asic Concepts in Computational Physics Second Edition
Basic Concepts in Computational Physics
Benjamin A. Stickler • Ewald Schachinger
Basic Concepts in Computational Physics Second Edition
123
Ewald Schachinger Institute of Theoretical and Computational Physics Graz University of Technology Graz, Austria
Benjamin A. Stickler Faculty of Physics University of Duisburg-Essen Duisburg Germany
Supplementary material and data can be found on link.springer.com ISBN 978-3-319-27263-4 DOI 10.1007/978-3-319-27265-8
ISBN 978-3-319-27265-8 (eBook)
Library of Congress Control Number: 2015959954 © Springer International Publishing Switzerland 2014, 2016 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 This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Preface
Traditionally physics is divided into two fields of activities: theoretical and experimental. As a consequence of the stunning increase in computer power and of the development of more powerful numerical techniques, a new branch of physics was established over the last decades: Computational Physics. This new branch was introduced as a spin-off of what nowadays is commonly called computer simulations. They play an increasingly important role in physics and in related sciences as well as in industrial applications and serve two purposes, namely: • Direct simulation of physical processes such as ı Molecular dynamics or ı Monte Carlo simulation of physical processes • Solution of complex mathematical problems such as ı Differential equations ı Minimization problems ı High-dimensional integrals or sums This book addresses all these scenarios on a very basic level. It is addressed to lecturers who will have to teach a basic course/basic courses in Computational Physics or numerical methods and to students as a companion in their first steps into the realm of this fascinating field of modern research. Following these intent
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