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Lagrangian and Hamiltonian Analytical Mechanics: Forty Exercises Resolved and Explained

  • Vladimir Pletser

Part of the UNITEXT for Physics book series (UNITEXTPH)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Vladimir Pletser
    Pages 1-18
  3. Vladimir Pletser
    Pages 19-24
  4. Vladimir Pletser
    Pages 25-38
  5. Vladimir Pletser
    Pages 51-90
  6. Vladimir Pletser
    Pages 91-124
  7. Back Matter
    Pages 125-128

About this book

Introduction

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.

Keywords

Hamilton-Jacobi equations Harmonic Oscillator Variational Principle Fermat Principle Canonical Transformations Schrödinger Equation Stark Effect Advance of Mercury perihelion

Authors and affiliations

  • Vladimir Pletser
    • 1
  1. 1.PITC, Technology and Engineering Centre for Space UtilizationChinese Academy of SciencesBeijingChina

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-13-3026-1
  • Copyright Information Springer Nature Singapore Pte Ltd. 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-981-13-3025-4
  • Online ISBN 978-981-13-3026-1
  • Series Print ISSN 2198-7882
  • Series Online ISSN 2198-7890
  • Buy this book on publisher's site
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