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Elements of Analytical Dynamics

  • 1st Edition - January 1, 1976
  • Latest edition
  • Author: Rudolph Kurth
  • Editors: I. N. Sneddon, M. Stark
  • Language: English

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… Read more

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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

  • Edition: 1
  • Latest edition
  • Published: July 10, 2014
  • Language: English

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