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Classical Mechanics with Mathematica

Antonio Romano and Addolorata Marasco
Publication Date: 
Number of Pages: 
Modeling and Simulation in Science, Engineering and Technology
[Reviewed by
Scott Guthery
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I use Mathematica a lot.  It turns a mobile phone into the ultimate HP-35 and on the desktop does things with tables that bring Excel to its knees.  Thus, when the opportunity to review Classical Mechanics with Mathematica by Antonio Romano and Addolorata Marasco I put my card in the hat.

There are many Mathematica notebooks that demonstrate classical mechanics.  I might mention those of Sándor Kabai available on the Wolfram website as they include simple dynamic models being driven by the mathematics which certainly aid understanding of how the mathematics and the mechanics are reflections of one another.

Unfortunately, there is no Mathematica code in the Romano/Marasco book.  In fact, it is very hard to understand why "Mathematica" is in the title of the book.  At the end of the Preface we find

“... [the book] provides the names of many notebooks, written using Mathematica, that are relevant to several of the book’s chapters... The notebooks referring to the first part are Geometry, Weierstrass, Phase2D, and LinStab.  In particular, the notebook Phase2D contains two programs Phase2D and PolarPhase.  The other notebooks relate to the second part.”

Just names.  No code. No hints as to where one might obtain these notebooks.  The cover of the book boasts in all-caps "EXTRA ONLINE" but one has to do a deep dive on the Springer website to find the notebooks that go with the book.  To save you time should you purchase the book, they are here:

The book casts classical mechanics in au courant notation and abstraction. We find in passing Hodge star operators, Levi-Civita tensors, and microcanonical probability. The notebooks provide little more than saving one the trouble of typing in a small subset of these modern formulations.  The Geometry notebook, for example, ``evaluates the geometric characteristics of a manifold when its metric is given.''  If readers wish to use the mathematics in the book or the code in the notebooks to design a linkage or rig an animation they will have some challenging special-casing work ahead of them.  

But then, it is unlikely this was the author's intent.  The book is a review of modern abstract differential equations: definitions, axioms, theorems, and proofs.  The usual---dare I say, classical---approach. The odd examples from classical mechanics encountered along the way are so trivial that one never comes to appreciate how the generality of today's mathematics enables one to represent, understand, and utilize more complicated mechanics, classical or otherwise.

Scott Guthery runs Docent Press, publisher of books in the history of mathematics, computing, and technology.

See the table of contents at the publisher's web page.