Schaum's Outline of Lagrangian Dynamics (Schaum's Outline Series) [ペーパーバック]

If you would like to understand and know who to use Lagrange equation, look no further. This book provides both theory and practical application to Lagrange equation. The material converge is excellent and complete. The book is rich in examples and solved problem. It is a graduate level book but also very accessible to people with good background in Dynamics. I often refer to it when solving dynamic modeling of systems.

This Schaum's outline is OK if you have an engineer's interest in the subject, but it does not have the kinds of problems you typically encounter in the pure sciences. It is also not typical of the high quality you find in other Schaum's outlines.
In Lagrangian mechanics, the trajectory of an object is derived by finding the path which minimizes the action, a quantity which is the integral of the Lagrangian over time. The Lagrangian for classical mechanics is taken to be the difference between the kinetic energy and the potential energy.
This considerably simplifies many physical problems. For example, consider a bead on a hoop. If one were to calculate the motion of the bead using Newtonian mechanics, one would have a complicated set of equations which would take into account the forces that the hoop exerts on the bead at each moment. The same problem using Lagrangian mechanics is much simpler. One looks at all the possible motions that the bead could take on the hoop and mathematically finds the one which minimizes the action. There are fewer equations since one is not directly calculating the influence of the hoop on the bead at a given moment.
I don't think that this Schaum' outline does a good job of showing the difference in approach to these kinds of problems. Instead Newtonian and Lagrangian approaches to problems are all jumbled up together. Instead, I recommend that you type "Lagrangian Dynamics" into Google and look at some of the excellent sets of lecture notes available on-line. The online tutorial "A Crash Course in Lagrangian Dynamics" is particularly helpful. At only 18 pages it gets to the heart of the matter and contains some solved numerical examples.
As an aside, if you use Amazon's "search inside" function for this book you will be completely confused. The table of contents and "excerpt" shown are for this book. However, the "Surprise Me" sections are from "Schaum's Outline of Mathematica". If the student of Lagrangian dynamics electronically "thumbs" through this book and wonders what creating 3D graphics with Mathematica has to do with Lagrangian dynamics, the answer is "nothing" - this is an editing error courtesy of Amazon.

This is the best of Schaum's Outlines. Not only is the treatment of variational mechanics complete, with exposition on every major aspect of the derivation and solution dynamical equations, it does so while exceeding all junior-level texts on analytical mechanics. Its treatment of dissipation functions in chapter six, moreover, is better than the available graduate textbooks on the subject. This is the one workbook in the series that you must own for learning and for future reference.