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Analytical Mechanics

  • Textbook
  • © 2002

Overview

Authors:
  1. A. I. Lurie
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  • Translation of a famous book that belongs to the cultural heritage of Russian mechanics
  • Reference for classical and analytical approaches to all branches of mechanics
  • Gives deeper insight into theory and applications of Analytical Mechanics

Part of the book series: Foundations of Engineering Mechanics (FOUNDATIONS)

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-18
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  2. Basic definitions

    • A. I. Lurie
    Pages 19-46

  3. Rigid body kinematics — basic knowledge

    • A. I. Lurie
    Pages 47-109

  4. Theory of finite rotations of rigid bodies

    • A. I. Lurie
    Pages 111-149

  5. Basic dynamic quantities

    • A. I. Lurie
    Pages 151-202

  6. Work and potential energy

    • A. I. Lurie
    Pages 203-265

  7. The fundamental equation of dynamics. Analytical statics

    • A. I. Lurie
    Pages 267-301

  8. Lagrange’s differential equations

    • A. I. Lurie
    Pages 303-390

  9. Other forms of differential equations of motion

    • A. I. Lurie
    Pages 391-448

  10. Dynamics of relative motion

    • A. I. Lurie
    Pages 449-522

  11. Canonical equations and Jacobi’s theorem

    • A. I. Lurie
    Pages 523-584

  12. Perturbation theory

    • A. I. Lurie
    Pages 585-668

  13. Variational principles in mechanics

    • A. I. Lurie
    Pages 669-780

  14. Back Matter

    Pages 781-864
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Keywords

About this book

According to established tradition, courses on analytical mechanics include general equations of motion of holonomic and non-holonomic systems, vari­ ational principles, theory of canonical transformations, canonical equations and theory of their integration (the Hamilton-Jacobi theorem), integral in­ variants, theory of last multiplier and others. The fundamental laws of mechanics are taken for granted and are not subject to discussion. The present book is concerned with those issues of the above listed sub­ jects which, in the author's opinion, are most closely related to engineering problems. Application of the methods of analytical mechanics to non-trivial prob­ lems at the very stage of constructing the equations requires detailed knowl­ edge of the issues that are normally only briefly touched upon. With this perspective considerable attention is paid to ways of introducing the gener­ alised coordinates, the theory of finite rotation, methods of calculating the kinetic energy, the energy of accelerations, the potential energy of forces of various nature, and the resisting forces. These introductory chapters, which have to some extent independent significance, are followed by those on methods of constructing differential equations of motion for holonomic and non-holonomic systems in various forms. In these chapters the issues of their interrelations, determination of the constraint forces and some prob­ lems of analytical statics are discussed as well. It is thought useful to include geometric considerations of the motion of a material system as motion of the representative point in Riemannian space.

Reviews

From the reviews:

"This monumental treatise on analytical mechanics is a translation of the original Russian edition from 1961. … it contains a wealth of material on the classic theory of mechanics, and methods of formulating the equations of motion of mechanical systems. … This book … makes good background reading for anyone with an interest in the classical foundations of mechanics. The gradual build up to the general equations and principles, supplemented with many examples, prepares the reader well … ." (Steen Krenk, Journal of Vibration and Acoustics, April, 2004)

"This book is a translation of a book originally printed in Russian in 1961. It offers a treatment of the dynamics of mechanical systems. … Analytical Mechanics would be a useful reference book for a person who is interested in engineering dynamics. It could also serve as a textbook for a graduate course in engineering dynamics … ." (Richard H. Rand, SIAM Review, Vol. 45 (2), 2003)

"This textbook … represents the lectures of a late great scholar and teacher at the Saint-Petersburg Polytechnic Institute. … the work is of original conception and contains also original contributions of the author. … A great attention is paid to the statement of problems and to the construction of the corresponding equations of motion. The book could be of interest to a large circle of graduate students as well as to researchers in the field who wish to acquire a deeper insight into analytical mechanics." (P. Teodorescu, Zentralblatt MATH, Vol. 1015, 2003)

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