Analytical Mechanics

1. Auflage 2017
ISBN: 978-3-319-44490-1
Verlag: Springer International Publishing

Buch, Englisch, 349 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 5562 g

Reihe: Undergraduate Lecture Notes in Physics

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 supportthe exceptionally clear and concise treatment of Analytical Mechanics.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Helrich, Carl S.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Mechanik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Statik, Dynamik, Kinetik, Kinematik

Inhaltsverzeichnis

History.- Lagrangian Mechanics.- Hamiltonian Mechanics.- Solid Bodies.- Hamilton-Jacobi Approach.- Complex Systems.- Chaos in Dynamical Systems.- Special Relativity.- Appendices.- Differential of S.- Hamilton-Jacobi Equation.- With Variables p, q, q.- Zero-Component Lemma.- Maxwell Equations from Field Strength Tensor.- Differential Operators.- Answers to Selected Exercises. 

Über Autor(innen)

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.