© 2017

Analytical Mechanics


Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Carl S. Helrich
    Pages 1-49
  3. Carl S. Helrich
    Pages 51-92
  4. Carl S. Helrich
    Pages 93-120
  5. Carl S. Helrich
    Pages 121-165
  6. Carl S. Helrich
    Pages 167-214
  7. Carl S. Helrich
    Pages 215-228
  8. Carl S. Helrich
    Pages 229-246
  9. Carl S. Helrich
    Pages 247-304
  10. Back Matter
    Pages 305-349

About this book


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.



Textbook Mechanics Physics Textbook Analytical Mechanics Textbook Lagrangian Mechanics Textbook Hamiltonian Mechanics Textbook Hamilton Jacobi Textbook Nonlinear Dynamics

Authors and affiliations


About the authors

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.

Bibliographic information

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