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.
Inhalt
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