Elements of Analytical Dynamics

Elements of Analytical Dynamics

1st Edition - January 1, 1976

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  • Editors: I. N. Sneddon, M. Stark
  • eBook ISBN: 9781483151724

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Description

Elements of Analytical Dynamics deals with dynamics, which studies the relationship between motion of material bodies and the forces acting on them. This book is a compilation of lectures given by the author at the Georgia and Institute of Technology and formed a part of a course in Topological Dynamics. The book begins by discussing the notions of space and time and their basic properties. It then discusses the Hamilton-Jacobi theory and Hamilton's principle and first integrals. The text concludes with a discussion on Jacobi's geometric interpretation of conservative systems. This book will be of direct use to graduate students of Mathematics with minimal background in Theoretical Mechanics.

Table of Contents


  • Preface

    Chapter I. The Equations of Motion

    § 1. Space and Time

    § 2. Dynamical Systems of Particles

    § 3. Lagrangian Systems

    Chapter II. Hamilton-Jacobi Theory

    § 4. Hamilton's Equation

    § 5. Canonical Transformations

    § 6. Time-Dependent Completely Canonical Transformations

    § 7. Time-Independent Completely Canonical Transformations: Generating Functions

    § 8. Jacobi's Partial Differential Equation

    Chapter III. Hamilton's Principle and First Integrals

    § 9. Hamilton's Principle, Euler's Equations

    § 10. First Integrals

    § 11. Noether's Theorem

    § 12. Stability

    Chapter IV. Jacobi's Geometric Interpretation of Dynamics

    § 13. Maupertuis' Principle

    § 14. Riemannian Geometry

    § 15. Jacobi's Geometric Interpretation of Conservative Lagrangian Systems

    § 16. Spaces With Intrinsic Metrics

    § 17. A Generalization of Jacobi's Interpretation

    § 18. Concluding Remarks

    Exercises

    References

    Supplementary Literature

    Index

    Other Titles in the Series


Product details

  • No. of pages: 192
  • Language: English
  • Copyright: © Pergamon 1976
  • Published: January 1, 1976
  • Imprint: Pergamon
  • eBook ISBN: 9781483151724

About the Editors

I. N. Sneddon

M. Stark

About the Author

Rudolph Kurth

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