Analytical Dynamics: Theory and Applications

✍ Scribed by Mark D. Ardema

• Publisher: Springer
• Year: 2004
• Tongue: English
• Leaves: 343
• Edition: 1
• Category: Library

✦ Synopsis

This book takes a traditional approach to the development of the methods of analytical dynamics. After a review of Newtonian dynamics, the basic concepts of analytical dynamics - classification of constraints, classification of forces, virtual displacements, virtual work and variational principles - are introduced and developed. Next, Langrange's equations are derived and their integration is discussed. The Hamiltonian portion of the book covers Hamilton's canonical equations, contact transformations, and Hamilton-Jacobi theory. Also included are chapters on stability of motion, impulsive forces, and the Gibbs-Appell equation. Two types of examples are used throughout the book. The first type is intended to illustrate key results of the theoretical development, and these are deliberately kept as simple as possible. The other type is included to show the application of the theoretical results to complex, real-life problems. These examples are often quite lengthy, comprising an entire chapter in some cases.

✦ Table of Contents

Cover......Page 1
Contents......Page 4
Preface......Page 8
1. Review of Newtonian Dynamics......Page 13
2. Motion and Constraints......Page 58
3. Virtual Displacement and Virtual Work......Page 76
4. Variational Principles......Page 94
5. Generalized Coordinates......Page 111
6. Lagrange's Equations......Page 119
7. Formulation of Equations......Page 141
8. Integration of Equations......Page 159
9. Examples......Page 174
10. Central Force Motion......Page 187
11. Gyroscopic Motion......Page 197
12. Stability of Motion......Page 213
13. Impulsive Motion......Page 233
14. Gibbs-Appell Equations......Page 252
15. Hamilton's Equations......Page 267
16. Contact Transformations......Page 287
17. Hamilton-Jacobi Equation......Page 302
18. Approximation Methods......Page 323
Bibliography......Page 338
Index......Page 340