Classical Mechanics with Maxima

Classical Mechanics with Maxima
Author: Todd Keene Timberlake
Publisher: Springer
Total Pages: 267
Release: 2015-10-06
Genre: Science
ISBN: 1493932071

This book guides undergraduate students in the use of Maxima—a computer algebra system—in solving problems in classical mechanics. It functions well as a supplement to a typical classical mechanics textbook. When it comes to problems that are too difficult to solve by hand, computer algebra systems that can perform symbolic mathematical manipulations are a valuable tool. Maxima is particularly attractive in that it is open-source, multiple-platform software that students can download and install free of charge. Lessons learned and capabilities developed using Maxima are easily transferred to other, proprietary software.

Finite Elements Using Maxima

Finite Elements Using Maxima
Author: Andreas Öchsner
Publisher: Springer
Total Pages: 256
Release: 2019-05-21
Genre: Science
ISBN: 303017199X

This book provides a study aid on the finite element method. Based on the free computer algebra system “Maxima”, it presents routines to symbolically or numerically solve problems in the context of plane truss and frame structures. This allows readers to not only check classical “hand calculations” but also understand the computer implementation of the method. The mechanical theories focus on the classical one-dimensional structural elements, i.e. bars, Euler–Bernoulli and Timoshenko beams as well as their combination to generalized beam elements. Focusing on one-dimensional elements reduces the complexity of the mathematical framework and the resulting matrix equations can still be displayed with all components, and not only in a symbolic representation. The use of a computer algebra system and the incorporated functions, e.g. for equation solving, highlights the methodology of the finite element method rather than standard procedures. The book is based on the Springer Brief “Finite Elements for Truss and Frame Structures” (978-3-319-94940-6) by the same authors.

Classical Mechanics

Classical Mechanics
Author: Matthew J. Benacquista
Publisher: Springer
Total Pages: 554
Release: 2018-02-27
Genre: Science
ISBN: 3319687808

This textbook provides an introduction to classical mechanics at a level intermediate between the typical undergraduate and advanced graduate level. This text describes the background and tools for use in the fields of modern physics, such as quantum mechanics, astrophysics, particle physics, and relativity. Students who have had basic undergraduate classical mechanics or who have a good understanding of the mathematical methods of physics will benefit from this book.

Classical Mechanics with Calculus of Variations and Optimal Control

Classical Mechanics with Calculus of Variations and Optimal Control
Author: Mark Levi
Publisher: American Mathematical Soc.
Total Pages: 322
Release: 2014-03-07
Genre: Mathematics
ISBN: 0821891383

This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.

Solved Problems in Classical Mechanics

Solved Problems in Classical Mechanics
Author: O.L. de Lange
Publisher: Oxford University Press
Total Pages: 608
Release: 2010-05-06
Genre: Mathematics
ISBN: 0199582521

simulated motion on a computer screen, and to study the effects of changing parameters. --

Classical Mechanics

Classical Mechanics
Author: Jan Awrejcewicz
Publisher: Springer Science & Business Media
Total Pages: 453
Release: 2012-07-26
Genre: Science
ISBN: 1461437911

This is the first volume of three, devoted to Mechanics. This book contains classical mechanics problems including kinematics and statics. It is recommended as a supplementary textbook for undergraduate and graduate students from mechanical and civil engineering, as well as for physical scientists and engineers. It contains a basic introduction to classical mechanics, including fundamental principles, statics, and the geometry of masses, as well as thorough discussion on kinematics.

Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics
Author: V. I. Arnold
Publisher: Springer Science & Business Media
Total Pages: 469
Release: 2013-11-11
Genre: Mathematics
ISBN: 1475716931

Many different mathematical methods and concepts are used in classical mechanics: differential equations and phase ftows, smooth mappings and manifolds, Lie groups and Lie algebras, symplectic geometry and ergodic theory. Many modern mathematical theories arose from problems in mechanics and only later acquired that axiomatic-abstract form which makes them so hard to study. In this book we construct the mathematical apparatus of classical mechanics from the very beginning; thus, the reader is not assumed to have any previous knowledge beyond standard courses in analysis (differential and integral calculus, differential equations), geometry (vector spaces, vectors) and linear algebra (linear operators, quadratic forms). With the help of this apparatus, we examine all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the hamiltonian formalism. The author has tried to show the geometric, qualitative aspect of phenomena. In this respect the book is closer to courses in theoretical mechanics for theoretical physicists than to traditional courses in theoretical mechanics as taught by mathematicians.

Introduction to Classical Mechanics

Introduction to Classical Mechanics
Author: Roy, Nikhil Ranjan
Publisher: Vikas Publishing House
Total Pages: 350
Release:
Genre: Technology & Engineering
ISBN: 932599402X

The book deals with the mechanics of particles and rigid bodies. It is written for the undergraduate students of physics and meets the syllabus requirements of most Indian universities. It also covers the entire syllabus on classical/analytical mechanics for various national and state level examinations like NET, GATE and SLET. Some of the topics in the book are included in the curricula of applied mathematics in several institutions as well. KEY FEATURES • Main emphasis is on the evolution of the subject, the underlying ideas, the concepts, the laws and the mathematical methods • Written in the style of classroom teaching so that the students may benefit from it by way of self-study • Step-by-step derivation of concepts, with each step clearly numbered • Concepts explained with the help of relevant examples to aid understanding

Introduction to Classical Mechanics

Introduction to Classical Mechanics
Author: Jain, Pushpendra K.
Publisher: Mkuki na Nyota Publishers
Total Pages: 362
Release: 2019-05-22
Genre: Science
ISBN: 9987083706

This book introduces Tanzanian students to the fascinating world of Mechanics - the science of motion and equilibrium. Concepts of mechanics namely vector and scalar quantities, forces, the laws of motion, work, energy, the conservation laws, gravitation, circular, orbital and oscillatory motions cut across not only most branches of physics such as electromagnetism, atomic, molecular, nuclear, astro and space physics, but are also applied to most branches of engineering and technology. This makes mechanics an important component of physics which students must master well at an early stage before branching to various career options. That is why undergraduate programs in sciences at most universities offer mandatory courses on basic mechanics within the first year of study. This book meets the needs of students and academics at the entry level courses. This book covers three crucial subareas of mechanics namely Kinematics, Newtonian mechanics and Lagrangian mechanics. Chapter 1 covers introductory aspects. Kinematics is discussed in chapter 2. Newton's laws of motion are introduced in chapter 3. Chapter 4 deals with the conservation of linear momentum. Work, energy and power are covered in chapter 5. Circular motion, Gravitation and planetary motion, and oscillations are covered in chapters 6, 7 and 8 respectively. Chapter 9 presents the aspects of rigid body dynamics, and Lagrangian mechanics is introduced in chapter 10, which lays a foundation for advanced courses in mechanics. The language of physics is universal, and the book is suited to students globally. However, the book recognises and addresses the specific needs of students in African Universities. There is a marked heterogeneity in the background of students ranging from those who are well prepared to those who are not so well prepared. The book meets the needs of all students. It presents detailed explanations of difficult-to-grasp topics with the help of simple but clearly drawn and labeled diagrams. The discussions and conclusions are presented point-wise, and key words, definitions, laws, etc., are highlighted. A unique feature of the book is a number of ‘Recipes’ which give students tailor made guidance to problems solving. Application of the recipe is illustrated by a solved example, followed by a similar exercise for students to practice. There are a large number of problems and exercises at the end of each chapter to further sharpen their skills.