Analytical Mechanics

Front Cover
Springer, Oct 1, 2016 - Science - 349 pages

This advanced undergraduate textbook begins with the Lagrangian formulation of Analytical Mechanics and then passes directly to the Hamiltonian formulation and the canonical equations, with constraints incorporated through Lagrange multipliers. Hamilton's Principle and the canonical equations remain the basis of the remainder of the text.

Topics considered for applications include small oscillations, motion in electric and magnetic fields, and rigid body dynamics. The Hamilton-Jacobi approach is developed with special attention to the canonical transformation in order to provide a smooth and logical transition into the study of complex and chaotic systems. Finally the text has a careful treatment of relativistic mechanics and the requirement of Lorentz invariance.

The text is enriched with an outline of the history of mechanics, which particularly outlines the importance of the work of Euler, Lagrange, Hamilton and Jacobi.

Numerous exercises with solutions support the exceptionally clear and concise treatment of Analytical Mechanics.

 

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Contents

1 History
1
2 Lagrangian Mechanics
50
3 Hamiltonian Mechanics
93
4 Solid Bodies
121
5 HamiltonJacobi Approach
167
6 Complex Systems
215
7 Chaos in Dynamical Systems
229
8 Special Relativity
247
Appendix B HamiltonJacobi Equation
310
Appendix C With Variables p q q
313
Appendix D ZeroComponent Lemma
317
Appendix E Maxwell Equations from Field Strength Tensor
319
Appendix F Differential Operators
321
Appendix G Answers to Selected Exercises
323
References
339
Index
343

Appendix A Differential of S
305

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About the author (2016)

Prof. Dr. Carl S. Helrich is professor emeritus from Goshen College (USA) with research interests in Condensed Matter Physics, Mathematical Physics and Computational Physics. He received his PhD in Theoretical Plasma Physics from Northwestern University (USA). More than 25 years of teaching experience at Tennessee Space Institute (USA), Research Laboratory Jülich (Germany), Bethel College in Kansas and Goshen College allow for a unique perspective to present analytical mechanics.