- Taschenbuch: 299 Seiten
- Verlag: Eurospan (30. März 2014)
- Sprache: Englisch
- ISBN-10: 0821891383
- ISBN-13: 978-0821891384
- Größe und/oder Gewicht: 1,9 x 14,6 x 21,6 cm
- Durchschnittliche Kundenbewertung: Schreiben Sie die erste Bewertung
- Amazon Bestseller-Rang: Nr. 213.704 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)
Classical Mechanics with Calculus of Variations and Optimal Control (Student Mathematical Library, Band 69) (Englisch) Taschenbuch – 30. März 2014
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Über den Autor und weitere Mitwirkende
Mark Levi , Pennsylvania State University, University Park, PA, USA
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For those who enjoyed reading "The Mathematical Mechanic" and "Why Cats Land on Their Feet", I have a note of caution: this is not Vol.3 of the trilogy.
If you can, try browsing through the book before buying it.
The cover of the book shows a toy gyroscope, lots of pulleys, a couple of monkeys on a rope, some Lissajous figures, etc, which all spell "high school physics". Since the previous two books by the same author were indeed accessible to high school graduates with some knowledge of vector algebra, it is possible to assume this book is likewise accessible to the same readers. It is not. Those most likely to appreciate it will be academics who already know the subject matter and will enjoy some fresh points of view, but for the student eager to get insight into some difficult concepts it will not be easy reading without a teacher's help.
The author mentions that the book might be used in conjunction with courses in topics mentioned in the title, for students exposed to (among other things) vector calculus. Semantics is important here, since the needed material is generally known as "vector analysis". The reader who is not a student and does not benefit from the help of an instructor, needs to be well acquainted with vector analysis, that is, with the notions of "div", "curl" and especially with Hamilton's "nabla" or "del" operator, which is used a lot in the book.
The text is based on course notes and sometimes the conversion must have been done in a great hurry, as I have the impression from the proof of Kepler's trajectories.
I looked for subjects that I was somewhat familiar with in order to get an idea about the book. For example, the "short" proof that Kepler's trajectories are conics at p.96 takes five pages of text, which is about as long as the "long" proof one can find in "Principles of Dynamics" by D.T. Greenwood or in "Newtonian Mechanics" by A.P. French.
The intuitive aspect of the explanation has to do with the trajectory being the result of two equations, describing a cone and a plane, the intersection of which results in a conic. In the process, out of the hat jump a new variable and an equation which we are promised will be proven "shortly", then just one line of text later, a statement is made about two linearly independent solutions, which we are told, will be explained two pages later. When you get there you find a brief talk about how linearly independent solutions are like vectors that are not parallel in the phase plane. So much for an "intuitive" explanation !
One of the mechanical phenomena that begs for an intuitive explanation is the gyroscopic effect, and not by accident a gyroscope has central place on the cover of the book. The truly intuitive explanation in the book is well known and is presented the same way in "Feynman's Lectures on Physics" Vol.1, p.20-6 as well as in "Why Cats Land on Their Feet" at p.112. The idea is that the speed vector of a rotating point of matter from the gyroscope is deflected by the precession rotation and produces the counterintuitive result, that the torque is at 90 degrees relative to precession axis.
Calculating the torque (as the author encourages the reader to do in Remark 3.3 at p.155) I found out the result to be only half of the true value. This is described in the book as "a not so easy challenge" but it is actually quite easy to do. What was not easy, was to find out where the other half of the torque was hiding. In the end I found the answer in "A Treatise on Gyrostatics and Rotational Motion" by A. Gray, available on Amazon. The explanation and proof are at pp.64-66.
What is missing from the well known but simplified analysis, is the fact that the speed vector also has a smaller perpendicular component due to the precession. The point of matter moves very fast due to the gyroscope's rotation so the radius of the point relative to the precession axis varies very fast which causes a change in speed, that is, an acceleration. The end result of this calculation is the missing half of the torque. So the intuitive explanation in the book is true but incomplete. Gray's book is a good reference for intuitively understanding both aspects of the gyroscopic effect.
As a final comment, I think that since Noether's theorem is mentioned no fewer than six times, a short biographical profile of Emmy Noether wouldn't have been out of place in the book. According to the Wikipedia, she was described as the most important woman in the history of mathematics. A good editor with enough time available wouldn't have missed it.
he has merely stated the result in a different language. This leaves the reader
desiring a full explanation completely on his own to hunt down supplementary
The second big drawback here is the lack of solutions to the many problems
at the end of sections. Again, no hints or suggestions of where to look for
more are given.
Finally, was the editor out to lunch when this was printed? It could easily have
been made into a more polished work with a little effort .
been made into a more finished and professional work .
In short this is one of the best book to learn mechanics. I wish one day all the books on physics and maths may be like this one.
But ... it has a ridiculous little dimension (in size). This implies that the letter be small, with a tiny type about 8 or 9. The foot notes (that there are a lot) are practically impossible to read them without a magnifying glass.
It's a shame that such a marvellous book must have an edition so bad. Very badly by the AMS. Nothing to do with the good editions of latest author's books with Princeton University Press.
I hope in future editions they can offer us a good large hardcover book carefully edited.
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