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07/11/2008 -
Classical Mechanics (2006)
by R. Douglas Gregory
ISBN0-521-53409-7. Cambridge University Press, Cambridge, United Kingdom. 2006. Softcover. 596 pages. $60.00.
Classical Mechanics by Prof. R. Douglas Gregory from the University of Manchester is a great introduction book on the basics of mechanics for college undergraduates. The whole book starts from the very basic concepts in classical mechanics, the well-known Newton’s laws of motion and the law of gravitation. Readers with no prior knowledge of the subject may find this part really helpful in laying the necessary background for the following chapters. Different topics in simple Newtonian mechanics such as linear oscillations, energy conservation, and non-linear oscillations, etc. are discussed in the first part. Very interesting examples like space travel, to be more specific, the calculation of Hohmann transfer orbit, and differential scattering cross section of Rutherford scattering in solid physics are also introduced.
The second part of this book talks about the more complicated multi-particle system problem. If the readers already have full knowledge of the mechanics of a single particle from part one, this second part will be very easy to grasp. This part begins by the introduction of the energy principle for a multi-particle system, the potential energy and energy conservation. And that is followed by the linear momentum principle. Important applications of this principle, such as rocket motion, collision theory, and the two-body problem are also introduced. The last chapter in this part talks about the angular momentum principle, which is not an easy subject. Interesting topics include the angular momentum principle and the planar rigid body motion.
The first two parts of the book talk about the simplified theories in classical mechanics; those principles are applicable only to some ideal situations. So in the third part, a general method derived by d’Alembert, Lagrange, the equations of motion, are introduced. This method is general and can be used to solve very complicated problems in real life. After defining a few basic concepts such as the generalized coordinates and the configuration space, the famous Lagrange’s equations are discussed. This equation may seem to be very mathematical and complicated for the first time readers; nevertheless, they are extremely important and are the basic of analytical mechanics. Thus a good understanding of this theory is essential. The last two chapters of this part are about a more general and fundamental theory, Hamilton’s principle—the basic for classical mechanics.
Finally, the fourth part of this book focuses on some related applications of all these theories. Small oscillations, rigid body kinematics and rigid body dynamics, etc. are discussed in this part. Readers may find very interesting examples of calculating winds, ocean currents, and bathwater motion by analogy with particle dynamics. Also, those who are interested in texture development in engineering will find Euler’s equations for the rotational motion of a rigid body very important and useful.
Overall, this is a well-organized book for classical mechanics with clear structure, accurately set problems, and also computer-assisted problems. Self-learning readers will also find the answers for the problem set at the back of the book helpful. It is worth mentioning that a strong mathematical background is needed to fully understand the whole book. With all that being said, I sincerely recommend this book by Prof. R. Douglas Gregory to everyone who needs a solid understanding of classical mechanics.
For more on Classical Mechanics, visit the Cambridge University Press web site.
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