An introduction to analytical mechanics

Bok, 2009

The present edition of this compendium is intended to be a complement to the textbook “Engineering Mechanics” by J.L. Meriam and L.G. Kraige (MK) for the course ”Mekanik F del 2” given in the first year of the Engineering physics (Teknisk fysik) programme at Chalmers University of Technology, Gothenburg. Apart from what is contained in MK, this course also encompasses an elementary understanding of analytical mechanics, especially the Lagrangian formulation. In order not to be too narrow, this text contains not only what is taught in the course, but tries to give a somewhat more general overview of the subject of analytical mechanics. The intention is that an interested student should be able to read additional material that may be useful in more advanced courses or simply interesting by itself. The chapter on the Hamiltonian formulation is strongly recommended for the student who wants a deeper theoretical understanding of the sub ject and is very relevant for the connection between classical mechanics (”classical” here denoting both Newton’s and Einstein’s theories) and quantum mechanics. The mathematical rigour is kept at a minimum, hopefully for the benefit of physical understanding and clarity. Notation is not always consistent with MK; in the cases it differs our notation mostly conforms with generally accepted conventions. The text is organised as follows: In Chapter 1 a background is given. Chapters 2, 3 and 4 contain the general setup needed for the Lagrangian formalism. In Chapter 5 Lagrange’s equation are derived and Chapter 6 gives their interpretation in terms of an action. Chapters 7 and 8 contain further developments of analytical mechanics, namely the Hamiltonian formulation and a Lagrangian treatment of constrained systems. Exercises are given at the end of each chapter. Finally, a translation table from English to Swedish of some terms used is found. Many of the exercise problems are borrowed from material by Ture Eriksson, Arne Kihlberg and Göran Niklasson. The selection of exercises has been focused on Chapter 5, which is of greatest use for practical applications.