Analytical mechanics : an introduction

著者

書誌事項

Analytical mechanics : an introduction

Antonio Fasano, Stefano Marmi ; translated by Beatrice Pelloni

(Oxford graduate texts)

Oxford University Press, 2013

  • : pbk

タイトル別名

Meccanica Analitica

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注記

Includes bibliographical references (p. [749]-758) and index

"First published in English 2006, first published in paperback 2013"--T.p. verso

内容説明・目次

内容説明

Analytical Mechanics is the investigation of motion with the rigorous tools of mathematics, with remarkable applications to many branches of physics (Astronomy, Statistical and Quantum Mechanics, etc.). Rooted in the works of Lagrange, Euler, and Poincare, it is a classical subject with fascinating developments and still rich with open problems. It addresses such fundamental questions as: Is the solar system stable? Is there a unifying "economy" principle in mechanics? How can a point mass be described as a "wave"? This book was written to fill a gap between elementary expositions and more advanced (and clearly more stimulating) material. It takes the challenge to explain the most relevant ideas and to show the most important applications using plain language and "simple" mathematics, often through an original approach. Basic calculus is enough for the reader to proceed through the book and when more is required, the new mathematical concepts are illustrated, again in plain language. The book is conceived in such a way that some difficult chapters can be bypassed, whilst still grasping the main ideas. However, anybody wishing to go deeper in some directions will find at least the flavour of recent developments and many bibliographical references. Theory is always accompanied by examples. Many problems are suggested and some are completely worked out at the end of each chapter. The book may effectively be used (and it is in several Italian Universities) for undergraduate as well as for PhD courses in Physics and Mathematics at various levels.

目次

  • 1. Geometric and kinematic foundations of Lagrangian mechanics
  • 2. Dynamics: general laws and the dynamics of a point particle
  • 3. One-dimensional motion
  • 4. The dynamics of discrete systems. Lagrangian formalism
  • 5. Motion in a central field
  • 6. Rigid bodies: geometry and kinematics
  • 7. The mechanics of rigid bodies: dynamics
  • 8. Analytical mechanics: Hamiltonian formalism
  • 9. Analytical mechanics: variational principles
  • 10. Analytical mechanics: canonical formalism
  • 11. Analytical mechanics: Hamilton-Jacobi theory and integrability
  • 12. Analytical mechanics: canonical perturbation theory
  • 13. Analytical mechanics: an introduction to ergodic theory and to chaotic motion
  • 14. Statistical mechanics: kinetic theory
  • 15. Statistical mechanics: Gibbs sets
  • 16. Lagrangian formalism in continuum mechanics
  • Appendices

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詳細情報

  • NII書誌ID(NCID)
    BB19213212
  • ISBN
    • 9780199673858
  • LCCN
    2005028822
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 原本言語コード
    ita
  • 出版地
    Oxford
  • ページ数/冊数
    xiii, 772 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
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