This is the first book review on the books I listed here that are good for stu­dents. The first sub­ject is clas­si­cal dynam­ics, on which I rec­om­mended two books. The book I am gonna review in this post is "Clas­si­cal Dynam­ics" by Don­ald T. Green­wood, Dover Publication.

This is a con­cise book, whose main text con­tains 324 pages. Such a small size gives stu­dents con­fi­dence to read it cover to cover. regard­ing the math­e­mat­i­cal pre­req­ui­site, although it claims to be a grad­u­ate textbook, it assumes only famil­iar­ity with basic cal­cu­lus and some knowl­edge in dif­fer­en­tial equations.

The book is very well orga­nized into seven chap­ters. The first chap­ter intro­duces basic con­cepts such as gen­er­al­ized coor­di­nates, con­straints, vir­tual work, and so on that are essen­tial and enough for the fol­low­ing chap­ters. Chap­ter two derives Lagrange's equa­tions, dis­cusses inte­grals of motion, and applies the the­ory to small oscil­la­tions. Many inter­est­ing exam­ples are worked out in this chap­ter. Chap­ter 3 then ana­lyzes four spe­cial appli­ca­tions of Lagrange's equa­tions, namely Rayleigh's Dis­si­pa­tion Func­tions, Impul­sive Motion, Gyro­scopic Sys­tems, Velocity-Dependent Potentials.

Chap­ter 4 turns to the other pil­lar of the the­ory of clas­si­cal dynam­ics: Hamilton's equa­tions. It first elab­o­rates the Hamilton's prin­ci­ple with log­i­cal clar­ity, then derives Hamilton's equa­tions with exam­ples. Finally, it dis­cusses other vari­a­tional prin­ci­ples and Liouville's theorem.

Chap­ters 5 and 6 should be con­sid­ered as a whole. Chap­ter 5 tells one how to obtain prin­ci­pal func­tions and char­ac­ter­is­tic func­tions by using the Hamilton-Jacobi method. Chap­ter 6 explores the the­ory of canon­i­cal trans­for­ma­tions and its appli­ca­tion to dyanam­ics in more details and in a gen­er­al­ized way, in vew­ing that a prin­ci­ple func­tion is a gen­er­at­ing func­tion for a canon­i­cal trans­for­ma­tion between two points in phase space. These two chap­ters con­tain lots of details that are worth read­ing carefully.

The last one, Chap­ter 7 dis­cusses spe­cial rel­a­tiv­ity by apply­ing pre­vi­ously intro­duced meth­ods. How­ever, I found that such a chap­ter is actu­ally not very nec­es­sary, at least for me. If one did not know much spe­cial rel­a­tiv­ity, he/she would not expect to learn much from this chap­ter. If one knew spe­cial rel­a­tiv­ity very well, then he/she should sim­ply skip the chap­ter. But any­way, if you like, it is still fun to read it.

Now, pros and cons. Com­pared to other polu­lar or stan­dard books on this sub­ject, this book is very well bal­anced between vol­ume, con­cise­ness, and the amount of details, it is easy to read. The book works every exam­ple in a detailed and heuris­tic way, which are good for the read­ers to develop their own problem-solving skills. The pic­to­r­ial illus­tra­tions in the book are also very nice. At the end of each chap­ter, there are a bunch of excer­cise prob­lems care­fully cho­sen by the author. Final resutls of these prob­lems are given at the end of the book so that read­ers can check their own answers after work­ing through the solu­tions by them­selves. I found that these prob­lems are extremely use­full and inter­est­ing; hence, I solved each of them step by step.

Frankly speak­ing, I did not find any non­neg­li­gi­ble dis­ad­van­tage of this book. Some­one has a review on Amzaon​.com, say­ing that "it fails to address issues like how one can use Lagrange's equa­tions (or Hamilton's, for that mat­ter) to cor­rectly account for the effects of non­lin­ear dis­si­pa­tive forces". But I dis­agree, because I think top­ics like non­lin­ear sys­tem should be bet­ter treated in a more con­tem­po­rary method, e.g. in the book: Clas­si­cal Dynam­ics: a con­tem­po­rary approach, which is the tar­get of my next book review.

You may feel that the book is a bit too old, since it was first pub­lished in 1977. But come on, the sub­ject is Clas­si­cal dynam­ics, on which a book can never be too old to read. Another over­whelm­ing rea­son to own it is that it is priced at only 10.37USD. Can any­body con­vince me to give up this one and buy the 100USD Goldstein's book instead? No way, of course not.

By the way, would any­one read the book and have trou­ble in solv­ing any of the prob­lem, please con­tact me, I can share my solu­tions with you.

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