Classical Mechanics: Theory and Mathematical Modeling (Cornerstones)

This approach together with the careful and pedagogical nature of the text makes the book, in particular, accessible to students of the applied sciences.

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My overall impression is that the book is strong in its discussion of interesting applications of rigid body mechanics Another strong point is the extremely rich collection of historical references in the bibliography. The text covers the classical topics A remarkable feature of this book is the extensive bibliography, covering five centuries of mechanics The author has developed an approach to the subject that has a distinct flavor and a style of its own.

Each chapter has a 'Problems and Complements' section that includes exercises and additional exposition related to the contents of that chapter.

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The approach intends to be more mathematical and the choice of subjects will generally appeal more to mathematics and physics students. My overall impression is that the book is strong in its discussion of interesting applications of rigid body mechanics …. The text covers the classical topics … and is couched in the language of vector calculus and linear algebra, making it accessible to graduate students in applied mathematics and physics. Joris Vankerschaver, Mathematical Reviews, Issue e.

Harry Potter Years by J. Rowling , Hardcover The first edition of this text was meant to fill a void in graduate education-the lack of a cogent text in the classical underpinnings of quantum mechanics like Hamiltonians and Poisson brackets-as other reviewers have indicated.

Classical Mechanics: Theory and Mathematical Modeling (Cornerstones)

This second edition serves that purpose also but goes beyond into applications of classical mechanics proper. The reader is assumed to have some proficiency in math analysis-implicit function theorem for example-enough to follow a proof say when you look it up. Luckily most all if you look hard enough of this math is available on the internet. In my day reference books were taken out excessively long in an effort to wipe out competition-nasty brats! Anyway this philosophy of evading rigorous math and relegating it to references persists to this day-many physicists have this belief that rigor restrains theoretical creativity-yeah there was some drug use back then.

Goldstein gives a reference to Euler's theorem on homogeneous functions in chapter 2-WTF! To make this exciting here's the proof: If you multiply each variable of the homogeneous function by t say the result after some algebra is t to some power called the degree times the original function.

Classical Mechanics: Theory and Mathematical Modeling (Cornerstones) | Souq - UAE

If we take the partial derivative with respect to t on both sides of this equation-on the left we use the chain rule in multivariable calculus-on the right we get a term that's the usual derivative of a power of t. This is done largely here in words but in math symbols it's shorter and not much more than the reference citation.

I'm not faulting the author since this was the in-thing back then as well as belief that fluency in math could not be assumed of the physics or engineering student. This is my second purchase of this text and my second reading-sold my first back to the college store.

I was nostalgic and also remembered the final chapter on the Lagrangian formulation of continuous fields to be quite good. There is an appendix in which is derived the acoustic field-gas is treated adiabatically and sound manifests as variations in density. Hamilton-Jacobi theory was corrected in this edition-the equation follows as a consequence of an equation relating the new Hamiltonian to the original and the generating function of its contact transformation.

Special relativistic mechanics is treated in chapter 7 and the reader is assumed to have previous exposure to the Lorentz transformation. Exercise 23 at the end of this chapter makes the reader derive the Ackeret equation, the relativistic analogue to the Tsiolkovsky rocket equation. Here you work in the center of mass frame of the rocket just before the particle or a particle is expelled from the rocket and you observe the energy and momentum consequences in this frame after expulsion keeping in mind that only first order terms in velocity and mass survive in the differential equation.

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The change in the rocket's velocity in this frame will be given as the ratio of the transformed x interval to the transformed t interval for motion along the x axis-this is a function of velocities seen in our fixed frame. Further the mass before expulsion had a rest mass energy in the center of mass frame and this energy must be equal the total energy of the expelled mass plus the kinetic energy now of the rocket in this center of mass frame.

This is a good problem to test your basic understanding of relativistic energy-momentum. Don't forget the momentum conservation equation-the energy equation gives you a relation between the expelled mass particle and the original mass particle to 1st order to be used in the momentum equation. Technically the center of mass frame does not exist in special relativity-multiple incompatible worldlines-we actually ride alongside the rocket just before the mass expulsion, an inertial frame and remain in this frame observing the energy and momentum consequences-it looks like the center of mass frame and it is non-relativistically in the Tsiolkovsky case.

It's that different behavior of momentum and energy as well as the different velocity addition law that fouls it up. The text gives many references for mechanics theorems which are hard to ferret out on your own. Also the only difference between this and the third edition is material on chaos and nonlinear dynamics which amounts to a greater emphasis on phase space-Liouville's theorem etc. Overall this edition then is worth having. Kindle Edition Verified Purchase. This book is a bit easier than Goldstein, whether that is good or bad depends on your personal preferences.

A deficiency is that in parts it becomes to abstract and short of concrete examples that are fully worked out. A problem with the Kindle version is that some of the mathematical notation has become mangled. This is a gold standard for the classical treatment of mechanics. I used it when I was a physics undergraduate and when I was a graduate student in engineering.

I still read it just to brush up on my mechanics.

This book is the Bible of Classical Mechanics. I still recognize new relations in this topic whenever I start to read it.