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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JakobIoannis PapadopoulosGriffEdiMichael Cohen Recent comment authors

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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 $\frac{\partial}{\partial \dot q}$.

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.

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.

Edi
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Edi

Congratulations to an excellent book! If you don’t mind, I have a question about the classical Lagrangian T-V. In Section 12.3.6 you show how the gravitational potential affects the proper time and thus gives rise to the –V term. However, my understanding is that the classical Lagrangian T-V hold for any type of potential, gravitational or non-gravitational. So, the following question arises: Do all kinds of potential, e.g., the electrostatic potential, affect the proper time? I know from your other book (Physics from Symmetry) that the Lagrangian of electromagnetic interactions can be obtained by making the U(1) symmetry of the… Read more »

Edi
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Edi

Thanks for the response Jakob! I thought some more about the -V term. Do you think the following line of reasoning is valid? (I am trying to make an argument similar to what you did in “Physics from Symmetry” sections 7.1.1-7.1.3, but for classical mechanics.) The classical free Lagrangian L = T = 1/2 m (dx/dt)^2 has the global symmetry L’ = L + a. Is this also a local symmetry: L’ = L + a(x)? No. Can we make it a local symmetry? Yes, if we add a term to the free Lagrangian, L = T – V(x), and… Read more »

Edi
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Edi

Thanks, Jakob! I have another question, if you don’t mind: On p.175, Eq.(7.129) you give an example of a generating function that flips the p’s and q’s. To get a better understanding, I tried to construct another example: as far as I can tell Q=k*q, P=p/k with parameter k is a canonical transformation, but I cannot construct the corresponding generating function F(q,Q). It seems to me that only certain canonical transformations (maybe only the ones that mix p’s and q’s) can be expressed in terms of generating functions. If this is so, what are the conditions? In contrast, I could… Read more »

Ioannis Papadopoulos
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Ioannis Papadopoulos

Compliments for your book and your extraordinary ability to write about difficult concepts in a very direct way. However, I have a question , the answer to which, I did not find in your book. Here is my question: When we derive Euler-Lagrange equations in classical mechanics following the Lagrangian approach we introduce Boundary conditions at the starting- and end-points of the path in the configuration space. Usually,though not necessarily, one requires that q(tinitial)=q(tfinal)=0, see section 4.3 of your book. But the standard problem in classical mechanics is to instead assume Initial (not Boundary) conditions, for instance it is assumed… Read more »