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

Elements of Analytical Dynamics, Volume 105

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


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



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.


Details

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

About the Editors

I. N. Sneddon Editor

M. Stark Editor

About the Authors

Rudolph Kurth Author