Bonus Material

No-Nonsense Classical Mechanics

  • A great visualization of the least-time principle in action can be found here.
  • A nice and very explicit discussion of the least action principle using interactive applets is available here.

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Phil
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Phil

Hello there. On p 84 the boxed comment states “All terms first order in epsilon must vanish.” I’m not really sure what the author means by this. I can see that if x = a is the lowest point, then for any epsilon (positive or negative), f(a) < f(a + epsilon). However, I don't really understand what the author means by "vanish". I suspect it's something quite straightforward that I'm not seeing, but if someone could flesh this out for me a bit, I would appreciate it.

Griff
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Griff

Hi Jakob, Thanks for writing these great books. They really help with getting the big picture of these subjects. I found a typo in the CM book, on page 157 in the derivation, in the step labelled ‘expanding the products,’ the term $ \frac{\partial \bar F}{\partial Q}\frac{\partial Q}{\partial p}\frac{\partial \bar H}{\partial Q}\frac{\partial Q}{\partial q}$ appears twice, but one of them should be $ \frac{\partial \bar F}{\partial Q}\frac{\partial Q}{\partial p}\frac{\partial \bar H}{\partial P}\frac{\partial P}{\partial q}$. The incorrect one is then retained in the cancellation in the next step. Do you have somewhere online where you post errata? That could help so… Read more »

Griff
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Griff

Oh, I thought the LaTeX would compile automagically :/

Griff
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Griff

On page 161, equation 7.88, you also have a $\frac{\partial}{\dot q}$ where it should be $\frac{\partial}{\partial \dot q}$.

philippe loutrel
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About Classical Mechanics
Not a very good book, an exceptional book, really!
It goes quite deep but you are helped all along with the margin notes: looks like the author reads our mind and he answers in these notes.
Also repeating an equation from previous pages is really convenient.
I am ordering right away the Quantum Mechanics book from the same author

Compared to Susskind Theoretical Minimum, i think this books goes into more details and is easier to follow.

Tamir
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Tamir

P.77 – “the ball cannot stay at the top indefinitely since we consider paths between a fixed initial position at fixed initial time and a fixed final position at a fixed final time.”
I dont get it. don’t thake into account the posibility of a constant function q(t)? Is there no stable equilibrium in the world?
sure I can see why it’s not even an equilibrium from newton perspective, but as for the lagrangian formulation it’s not clear…

Robert Herman
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Robert Herman

Great book for me! I am trying to relearn CM after decades, and the pace and clarity fit me well.

I’m pretty sure I know, but on page 34, (2.12) has force = to the first derivative of momentum, p,
or F= m*a.

Am I correct in assuming that when we take the first derivative of p, m just carries over, since the exponent of v time m = m?

I find this better than the Theoretical Minimum too, and plan on buying Mr. Schwichtenberg’s books!

Roy
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Roy

Hello, I will be using John Taylor’s CM next semester in a class. I am hoping this will allow me to get ahead instead of being behind.
Feel free to provide any advice.

Roy
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Roy

I purchased all three of your books.

Ronnie Webb
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Ronnie Webb

Hello and thank you for writing an amazing book on Classical Mechanics that even a self learner like myself can finally learn from! I have a question about the derivations of the q and p transformations via the Poisson Bracket (page 171). In the q derivation the bracket is {q, G}, but in the p derivation the bracket is {G, p}. The Poisson Bracket calculation on the next line (for the p transformation) under this portrays a different calculation i.e. it looks like it should be {p, G}. But, above all of this the equations say q+eG o q and… Read more »

Lucas
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Lucas

Jakob, on page 370 it seems that in order to obtain equation D.16 you had to assume that the partial derivative of (dx/dt)2 with respect to x and the partial derivative of x2 with respect to dx/dt are both zero. This makes sense if we assume that x and dx/dt are independent variables, but in page 95, when deriving Hamilton’s equations, you state clearly that it is “not possible” to treat x and dx/dt as “completely independent variables” “because the velocity is always simply the rate of change of the location”. If this is so, why can we assume that… Read more »

Lucas
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Lucas

Jakob, what is the order you recommend when reading your books? I intend to do Classical Mechanics, Electrodynamics, Quantum Mechanics and then Physics from Symmetry? Would you agree?

Michael Cohen
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Hi Jakob, At the bottom of page 164 to arrive at (7.98) you cancel a partial derivative of Q with a total derivative of Q. Is that allowed? Although final answer is correct it seems that is because the partial (p) of F/pQ x Qdot sums to zero with its equivalent in the parentheses. Your thoughts? Thank you. BTW loving the book.