Lagrangian and Hamiltonian Analytical Mechanics: Forty Exercises Resolved and Explained PDF Download
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Author: Vladimir Pletser
Publisher: Springer
ISBN: 9811330263
Category : Science
Languages : en
Pages : 128
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Book Description
This textbook introduces readers to the detailed and methodical resolution of classical and more recent problems in analytical mechanics. This valuable learning tool includes worked examples and 40 exercises with step-by-step solutions, carefully chosen for their importance in classical, celestial and quantum mechanics. The collection comprises six chapters, offering essential exercises on: (1) Lagrange Equations; (2) Hamilton Equations; (3) the First Integral and Variational Principle; (4) Canonical Transformations; (5) Hamilton – Jacobi Equations; and (6) Phase Integral and Angular Frequencies Each chapter begins with a brief theoretical review before presenting the clearly solved exercises. The last two chapters are of particular interest, because of the importance and flexibility of the Hamilton-Jacobi method in solving many mechanical problems in classical mechanics, as well as quantum and celestial mechanics. Above all, the book provides students and teachers alike with detailed, point-by-point and step-by-step solutions of exercises in Lagrangian and Hamiltonian mechanics, which are central to most problems in classical physics, astronomy, celestial mechanics and quantum physics.
Author: Vladimir Pletser
Publisher: Springer
ISBN: 9811330263
Category : Science
Languages : en
Pages : 128
Get Book
Book Description
This textbook introduces readers to the detailed and methodical resolution of classical and more recent problems in analytical mechanics. This valuable learning tool includes worked examples and 40 exercises with step-by-step solutions, carefully chosen for their importance in classical, celestial and quantum mechanics. The collection comprises six chapters, offering essential exercises on: (1) Lagrange Equations; (2) Hamilton Equations; (3) the First Integral and Variational Principle; (4) Canonical Transformations; (5) Hamilton – Jacobi Equations; and (6) Phase Integral and Angular Frequencies Each chapter begins with a brief theoretical review before presenting the clearly solved exercises. The last two chapters are of particular interest, because of the importance and flexibility of the Hamilton-Jacobi method in solving many mechanical problems in classical mechanics, as well as quantum and celestial mechanics. Above all, the book provides students and teachers alike with detailed, point-by-point and step-by-step solutions of exercises in Lagrangian and Hamiltonian mechanics, which are central to most problems in classical physics, astronomy, celestial mechanics and quantum physics.
Author: Melvin G. Calkin
Publisher: World Scientific
ISBN: 9789810237820
Category : Science
Languages : en
Pages : 244
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Book Description
This book contains the exercises from the classical mechanics text Lagrangian and Hamiltonian Mechanics, together with their complete solutions. It is intended primarily for instructors who are using Lagrangian and Hamiltonian Mechanics in their course, but it may also be used, together with that text, by those who are studying mechanics on their own.
Author: José Rachid Mohallem
Publisher: Springer Nature
ISBN: 3031552024
Category :
Languages : en
Pages : 150
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Book Description
Author: Ioan Merches
Publisher: CRC Press
ISBN: 148223940X
Category : Science
Languages : en
Pages : 456
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Book Description
Giving students a thorough grounding in basic problems and their solutions, Analytical Mechanics: Solutions to Problems in Classical Physics presents a short theoretical description of the principles and methods of analytical mechanics, followed by solved problems. The authors thoroughly discuss solutions to the problems by taking a comprehensive a
Author: Patrick Hamill
Publisher: Cambridge University Press
ISBN: 1107042887
Category : Mathematics
Languages : en
Pages : 185
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Book Description
A concise treatment of variational techniques, focussing on Lagrangian and Hamiltonian systems, ideal for physics, engineering and mathematics students.
Author: Nivaldo A. Lemos
Publisher: Cambridge University Press
ISBN: 1108265944
Category : Science
Languages : en
Pages : 475
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Book Description
Analytical mechanics is the foundation of many areas of theoretical physics including quantum theory and statistical mechanics, and has wide-ranging applications in engineering and celestial mechanics. This introduction to the basic principles and methods of analytical mechanics covers Lagrangian and Hamiltonian dynamics, rigid bodies, small oscillations, canonical transformations and Hamilton–Jacobi theory. This fully up-to-date textbook includes detailed mathematical appendices and addresses a number of advanced topics, some of them of a geometric or topological character. These include Bertrand's theorem, proof that action is least, spontaneous symmetry breakdown, constrained Hamiltonian systems, non-integrability criteria, KAM theory, classical field theory, Lyapunov functions, geometric phases and Poisson manifolds. Providing worked examples, end-of-chapter problems, and discussion of ongoing research in the field, it is suitable for advanced undergraduate students and graduate students studying analytical mechanics.
Author: Yiannis Menis
Publisher: ΔΩΡΕΑΝ
ISBN:
Category : Science
Languages : en
Pages : 160
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Book Description
History of Classical Mechanics Classical Mechanics is one of the most important foundations of theoretical physics. The term "Classical Mechanics" refers to the system of mathematical physics that began in the 17th century by Isaac Newton based on the astronomical theories of Johannes Kepler and Tycho Brahe. This theory has been expanded and reformed by Lagrange and Hamilton. Lagrangian Mechanics is one of the two fundamental branches of Analytical Dynamics along with Hamiltonian Mechanics. It was formulated by the French mathematician Lagrange in the period 1783-88. In 1755 the Euler - Lagrange equation appears. At that time, both 19-year-old Lagrange and 48-year-old Euler are looking for a solution to the "equinox problem." Lagrange arrives at a solution in 1755 and sends it to Euler who processes it in order to arrive at a formula based on the Principle of Least Action, according to which the path of a particle is the one that yields a stationary value of the action. Quantum Mechanics can be established with aforementioned principle in conjunction with path integrals. The latter were introduced by Dirac and Feynman. The study of the problems of classical mechanics continued in the 20th century by great mathematicians such as Henri Poincare, reaching to date with the non-linear dynamics and the introduction of the concept of Chaos. Classical Mechanics is an inexhaustible source of new issues and concerns. This book aspires to be a small aid in the hands of the reader who wishes to begin his work with this great piece of physics, with a brief but comprehensive reference to theory and a satisfactory collection of solved exercises. Book presentation This book consists of 143 solved problems, accompanied by several images designed to enhance the understanding of the exercises. The fundamental theory is presented in a question-and-answer format, and each exercise is accompanied by a set of remarks and reminders. "Lagrangian Mechanics: Problems and Solutions" is tailored for undergraduate students of Science and Polytechnics. Key Features 1. Solved Problems: The book contains 143 solved problems related to Lagrangian Mechanics. These problems are cover various aspects of the subject, allowing readers to practice and apply theoretical concepts to real-world scenarios. 2. Comprehensive Reference: The book serves as a comprehensive reference for Lagrangian Mechanics, covering fundamental theories and principles. It is to provide explanations of key concepts and equations, offering readers a solid foun-dation in the subject. 3. Question-and-Answer Format: The book present its content in a question-and-answer format, making it easier for readers to follow along and understand the material. This approach helps to engage readers actively in the learning process. 4. Images for Enhanced Understanding: The inclusion of images in the book may aid in visualizing the concepts and solutions. Diagrams, graphs, and illustrations can enhance the reader's understanding of the theoretical concepts and problem-solving techniques. 5. Remarks and Reminders: Each exercise may be accompanied by remarks and reminders, providing additional insights and clarifications related to the solved problems. These notes can help readers avoid common pitfalls and develop a deeper understanding of the solutions. 6. Tailored for Undergraduate Students: The book is be designed specifically for undergraduate students of Science and Polytechnics, with the level of content appropriate for those pursuing degrees in physics, engineering, mathematics, or related disciplines. 7. Practical Application: The book may emphasize practical application, focusing on how Lagrangian Mechanics principles are used in real-world scenarios and engineering applications. This approach can help readers see the relevance of the subject in various fields.
Author: Claude Gignoux
Publisher: Springer Science & Business Media
ISBN: 9048123933
Category : Science
Languages : en
Pages : 464
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Book Description
The aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.
Author: Antonio Fasano
Publisher: Oxford University Press
ISBN:
Category : Mathematics
Languages : en
Pages : 804
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Book Description
Is the solar system stable? Is there a unifying 'economy' principle in mechanics? How can a pointmass be described as a 'wave'? This book offers students an understanding of the most relevant and far reaching results of the theory of Analytical Mechanics, including plenty of examples, exercises, and solved problems.
Author: Carl S. Helrich
Publisher: Springer
ISBN: 3319444913
Category : Science
Languages : en
Pages : 349
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Book Description
This advanced undergraduate textbook begins with the Lagrangian formulation of Analytical Mechanics and then passes directly to the Hamiltonian formulation and the canonical equations, with constraints incorporated through Lagrange multipliers. Hamilton's Principle and the canonical equations remain the basis of the remainder of the text. Topics considered for applications include small oscillations, motion in electric and magnetic fields, and rigid body dynamics. The Hamilton-Jacobi approach is developed with special attention to the canonical transformation in order to provide a smooth and logical transition into the study of complex and chaotic systems. Finally the text has a careful treatment of relativistic mechanics and the requirement of Lorentz invariance. The text is enriched with an outline of the history of mechanics, which particularly outlines the importance of the work of Euler, Lagrange, Hamilton and Jacobi. Numerous exercises with solutions support the exceptionally clear and concise treatment of Analytical Mechanics.
