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- Classical
- Thread starter shinobi20
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both texts are not for mathematicians

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What do you mean by both text are not for mathematicians?both texts are not for mathematicians

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It is long to explain. I mean that both texts are below the mathematical standards of rigorWhat do you mean by both text are not for mathematicians?

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Arnold, Mathematical methods of classical mechanics, Springer

is a good choice. For a physicist it's also a good read after he or she is familiar with the physics.

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both texts are not for mathematicians

It is long to explain. I mean that both texts are below the mathematical standards of rigor

These two quotes mean different things.

I know a counter-example to the first quote.

I know someone who has a had long career as a university professor teaching and doing research in pure mathematics, and who likes to read theoretical physics books. For example, he loves "Introduction to Particle Physics" by Griffiths and "The Quantum Theory of Fields" by Weinberg. When I told him about mathematically more rigourous books, like "Quantum Theory for Mathematicians" by Hall or the forthcoming quantum field theory book by Talagrand on quantum field theory, he told me that he prefers standard physics books.

So, physics books are for him, yet he would be in complete agreement with the second quote.

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page 23:

The author suggests to consider variations of this functional in the class of curves with fixed ends in the phase space. It is pointless and it does not correspond to the well-known ##\int Ldt##.

Indeed, the Hamiltonian equations are of the first order and if you fix a point in the phase space you also fix a trajectory that passes through this point (existence and uniqueness theorem) . This trajectory is not obliged to pass through the second point you fixed. Moreover if you fix two arbitrary points in the phase space, the probability that these points are appeared to be connected by a solution to the Hamiltonian system, will be equal to zero. It is so even if the points are close to each other.

Thus the functional ##J## (according to this text) does not have stationary paths almost certainly. In the correct statement (see for example cited above Arnold's book) one fixes only ##q## positions at the ends of the path and does not fix impulses ##p##. This corresponds to the Lagrangian situation (##\int Ldt##) when we also fix ##q## positions and do not fix velocities ##\dot q##.

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Of course, one really understands why the boundary conditions in phase space are what they are when considering the derivation from the path integral of quantum theory (which is not mathematically rigorous either though).

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If I may ask, what is the relevance of the previous posts to the OP?

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https://www.amazon.com/dp/0198508026/?tag=pfamazon01-20

https://www.amazon.com/dp/0191001627/?tag=pfamazon01-20

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I've honestly spent a fair bit of time trying to learn from Goldstein, but for some reason was never really able to learn much from it - this is by far the best alternative I have found.

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How would you rate Oliver Johns' book?

https://www.amazon.com/dp/0198508026/?tag=pfamazon01-20

https://www.amazon.com/dp/0191001627/?tag=pfamazon01-20

I've honestly spent a fair bit of time trying to learn from Goldstein, but for some reason was never really able to learn much from it - this is by far the best alternative I have found.

So how do you compare Lemos' book with Goldstein's (Is it really that bad)? I've never heard of Lemos before but by looking it seems to follow the standard topics, and it looks promising.

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Yes, I saw you commenting in another post that he made a mistake regarding non-holonomic constraints but I do not know which part of the book you are pertaining, so now I know it is in the part of Hamilton's principle.

Do you know other flaws in Goldstein that I should watch out? Also, do you know any lecture notes that follow Goldstein's book and which writes correctly the part which Goldstein had written incorrectly?

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Do you know other flaws in Goldstein that I should watch out?

A minor flaw, but on page 4 of latest edition he writes that "infinitesimal" work done by a friction force is

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