Elements of Analytical Dynamics - 1st Edition - ISBN: 9780080198484, 9781483151724

Elements of Analytical Dynamics

1st Edition

Editors: I. N. Sneddon M. Stark
Authors: Rudolph Kurth
eBook ISBN: 9781483151724
Imprint: Pergamon
Published Date: 1st January 1976
Page Count: 192
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Table of Contents


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



Supplementary Literature


Other Titles in the Series


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.


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About the Editors

I. N. Sneddon Editor

M. Stark Editor

About the Authors

Rudolph Kurth Author