E-Book, Englisch, 192 Seiten, Web PDF
Kurth / Sneddon / Stark Elements of Analytical Dynamics
1. Auflage 2014
ISBN: 978-1-4831-5172-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 192 Seiten, Web PDF
Reihe: International Series in Pure and Applied Mathematics
ISBN: 978-1-4831-5172-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Elements of Analytical Dynamics;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;8
6;Chapter 1. The Equations of Motion;10
6.1;§ 1. Space and Time;10
6.2;§ 2. Dynamical Systems of Particles;18
6.3;§ 3. Lagrangian Systems;29
7;Chapter 2. Hamilton-Jacobi Theory;47
7.1;§ 4. Hamilton's Equation;47
7.2;§ 5. Canonical Transformations;55
7.3;§ 6. Time-Dependent Completely Canonical Transformations;70
7.4;§ 7. Time-Independent Completely Canonical Transformations: Generating Functions;77
7.5;§ 8. Jacobi's Partial Differential Equation;83
8;Chapter 3. Hamilton's Principle and First Integrals;91
8.1;§ 9. Hamilton's Principle, Euler's Equations;91
8.2;§10. First Integrals;93
8.3;§11. Noether's Theorem;111
8.4;§12. Stability;119
9;Chapter 4. Jacobi's Geometric Interpretation of Dynamics;131
9.1;§13. Maupertuis' Principle;131
9.2;§14. Riemannian Geometry;134
9.3;§15. Jacobi's Geometric Interpretation of Conservative Lagrangian Systems;144
9.4;§16. Spaces With Intrinsic Metrics;151
9.5;§17. A Generalization of Jacobi's Interpretation;158
9.6;§18. Concluding Remarks;162
10;Exercises;166
11;References;172
12;Supplementary Literature;180
13;Index;184
14;Other Titles in the Series;192
