Which classical mechanics book has better content?

[Val Antthony]

Hey guys! I'm currently on my junior year and I will be taking advanced classical mechanics next semester. My lectures will consist mainly on Lagrangian and Hamiltonian mechanics and I am currently in need of a good book in classical mechanics. I have used Kleppner and Kolenkow's An Introduction to Mechanics a year ago and I also have experience in vector calculus, differential equations, and linear algebra. Also, I'm going to take statistical mechanics, electrodynamics and quantum mechanics in the near future, so a good foundation in classical mechanics is needed.

1. Classical Mechanics 3rd Edition by Goldstein, Poole, Safko (They say that this is the golden standard of all the classical mech books)

2. Classical Mechanics 2nd Edition by Herbert Goldstein (I've heard that a chapter from the second edition was removed in the 3rd edition plus it's cheaper)

3. Classical Dynamics of Particles and Systems 5th Edition by Thornton and Marion

4. Classical Mechanics by Gregory

5. Classical Mechanics by Taylor (I've seen good reviews with this book)

 

[mpresic]

Classical Mechanics by Goldstein is an excellent graduate level textbook. However, unless your background is unusually thorough for a upper undergraduate (i.e. Junior), you are better off with a good intermediate textbook. By the way, I prefer Goldstein 2nd edition to Goldstein third edition, but not because it is cheaper. I do not think the additional material from the added authors works well with the classical mechanics as it was presented in the second edition. There was plenty of material in the second edition, that is skipped by instructors to get into the fashionable material on chaos etc.
I took chaos theory as a separate course and I think it belongs there, in favor or the advanced sections in Goldstein 2nd ed.

Back to your problem. I think Marion and Thornton is the best of the books you listed for classical mechanics at the Junior level. It introduces Lagrangian and Hamiltonian formulation.

Another book that I recommend that I studied for my quals is an older book by Symon. Later chapters in Symon treat the General Theory of Relativity.
(Interesting). I think Symon treats moment of inertia and rigid body motion in a clearer way than Marion and Thornton, but Marion and Thornton is also good.

I have seen the other two books (Gregory, and Taylor) but I am not as familiar with them. From what I remember, Marion and Thornton is better.

 

[Val Antthony]

I'll definitely look into the Symon book. Seems very interesting in my opinion. Thanks a lot!

 

[vanhees71]

Landau&Lifshitz vol. 1 is short and to the point.

 

[Val Antthony]

Totally forgot about this classic. Thanks!

 

[zwierz]

Arnold Math Methods of Classical Mechanics

 

[mpresic]

I would not recommend Landau and Livshitz Mechanics or Arnold's Classical Methods for a upper undergraduate mechanics course. Especially for someone that had their last Mechanics course, out of Kleppner and Kolenkow, more than a year ago.

Landau and Livshitz vol 1 is good, but it is too advanced for most undergraduates and too thin. Supplementing LL 1 with some material from LL2, classical theory of fields might work, but it is just too much a stretch from Kleppner and Kolenkow. Arnold might be a good book for a mathematical physicist but I would use it after a graduate text like Goldstein, certainly not before.

The OP mentioned learning classical mechanics as a prelude to later QM courses. This is a good idea. I should mention Shankar's book on quantum mechanics contains excellent preparatory review material on classical mechanics and math preliminaries before introducing the quantum postulates. In this regard, I find Shankar's treatment better than (the more common) Sakurai's

 

[Dr.D]

I'd like to suggest this one:
Dynamics of Mechanical and Electromechanical Systems
by Crandall, Karnopp, Kurtz, and Pridmore-Brown, McGraw-Hill, 1968.
It is no doubt out of print, but I'd think you could still find it used. It has a remarkably good presentation of energy methods, making very clear distinctions between energy and co-energy all the way through. I recommend it most strongly.

 

[smodak]

Don't forget Spivak . Somehow the Amazon Prices are crazy - not sure why.

 

[vanhees71]

The OP mentioned learning classical mechanics as a prelude to later QM courses. This is a good idea. I should mention Shankar's book on quantum mechanics contains excellent preparatory review material on classical mechanics and math preliminaries before introducing the quantum postulates. In this regard, I find Shankar's treatment better than (the more common) Sakurai's

But the more Landau/Lifshitz is the right choice. What you really need for QM is Hamiltonian mechanis in Poisson bracket formulation, and that's introduced quite well in Landau and Lifshitz. Arnold is great to, but way too far from standard-physics language to be of much help for studying QM. Of course, it's great to get the details about the mathematics behind the Hamiltonian formalism, i.e., the symplectic nature of phase space and all that. If you want to prepare in a more math-oriented way, I'd rather recommend to learn some basic theory about Lie groups and algebras and their representations (on the level of the good old book by Hamermesh or, more modern, Sexl&Urbandtke).

 

[Dr.D]

What you really need for QM is Hamiltonian mechanis in Poisson bracket formulation, and that's introduced quite well in Landau and Lifshitz

Does the OP want to learn classical mechanics, or does he simply want to prepare for quantum mechanics? He mentions that he intends to take QM, but I did not read that this was really the sine qua non.

 

[ChiralSuperfields]

I'd like to suggest this one:
Dynamics of Mechanical and Electromechanical Systems
by Crandall, Karnopp, Kurtz, and Pridmore-Brown, McGraw-Hill, 1968.
It is no doubt out of print, but I'd think you could still find it used. It has a remarkably good presentation of energy methods, making very clear distinctions between energy and co-energy all the way through. I recommend it most strongly.

What is co-energy?

 

[Demystifier]

What is co-energy?

I've also not heard of it before. After some googling, it seems to be a concept used by engineers. See e.g. https://en.wikipedia.org/wiki/Coenergy

 

[robphy]

Possibly enlightening…
(An old thread)
https://www.physicsforums.com/threa...2m-give-different-results.809914/post-5085857

 

[andresB]

What is co-energy?

For a system of variable mass, the Lagrangian function is the kinetic co-energy minus the potential energy. An important case is the relativistic Lagrangian
https://aapt.scitation.org/doi/10.1119/1.4885349

 

[vanhees71]

In relativistic mechanics $L \neq T-V$. In the (special-relativistic) (1+3)-formulation with the coordinate time and using the motion in an external em. field as the most simple example for an external field (interaction point-particle mechanics is always inconsistent and doesn't really exist ;-)) you have
$$L=-mc^2 \sqrt{1-\dot{\vec{x}}^2} -\frac{q}{c} A^0(t,\vec{x}) +\frac{q}{c} \vec{A}(t,\vec{x}) \cdot \dot{\vec{x}},$$
which leads to a Lorentz invariant and gauge-covariant action.

Are you saying that the first term is named "co-energy"? It's just a name or is it some deeper concept?

 

[andresB]

Are you saying that the first term is named "co-energy"? It's just a name or is it some deeper concept?

The general form of the Lagrangian function is $L=T^{*}-V$ where $T^{*}$ is a thing called the kinetic co-energy. It just so happens that $T^{*}=T$ in the non-relativistic case with constant mass.

The kinetic co-energy is mathematically well-defined, but I have no idea what is its physical interpretation. I recommend reading the paper I linked since it explains the situation much better than I could.

 

[robphy]

The kinetic co-energy is the Legendre transformation of the kinetic energy.

 

[vanhees71]

The general form of the Lagrangian function is $L=T^{*}-V$ where $T^{*}$ is a thing called the kinetic co-energy. It just so happens that $T^{*}=T$ in the non-relativistic case with constant mass.

The kinetic co-energy is mathematically well-defined, but I have no idea what is its physical interpretation. I recommend reading the paper I linked since it explains the situation much better than I could.

The reason that in Newtonian mechanics $T^*=T$ is of course that the kinetic energy is a quadradic form of the (generalized) velocities, i.e.,
$$T=\frac{1}{2} g_ij(q) \dot{q}^i \dot{q^j}.$$
This again follows from the specific spacetime symmetries of Newtonian mechanics, i.e., the full Galilei group with its 10 one-parameter subgroups leading to the conservation of energy, momentum, angular momentum, and center-of-mass velocity.

For relativistic mechanics that's no longer the case, and of course by definition what's called "Energy" is the quantity which is conserved due to translation invariance in time (a symmetry shared by both Newtonian and special-relativistic theory but in general not by general relativity).

It's indeed true that the physical meaning of the Lagrangian is in general not that obvious. It's just a function defining the action functional in terms of generalized coordinates and generalized velocities (this holds for all fundamental theories, including field theories). Its only purpose is to derive the equations of motion of the system, and its form is usually determined either by symmetry principles. In this sense it's not necessarily interpretible as an observable. It's also only defined up to a total time derivative of a function depending only on the generalized coordinates.

 

[MidgetDwarf]

Hey guys! I'm currently on my junior year and I will be taking advanced classical mechanics next semester. My lectures will consist mainly on Lagrangian and Hamiltonian mechanics and I am currently in need of a good book in classical mechanics. I have used Kleppner and Kolenkow's An Introduction to Mechanics a year ago and I also have experience in vector calculus, differential equations, and linear algebra. Also, I'm going to take statistical mechanics, electrodynamics and quantum mechanics in the near future, so a good foundation in classical mechanics is needed.

1. Classical Mechanics 3rd Edition by Goldstein, Poole, Safko (They say that this is the golden standard of all the classical mech books)

2. Classical Mechanics 2nd Edition by Herbert Goldstein (I've heard that a chapter from the second edition was removed in the 3rd edition plus it's cheaper)

3. Classical Dynamics of Particles and Systems 5th Edition by Thornton and Marion

4. Classical Mechanics by Gregory

5. Classical Mechanics by Taylor (I've seen good reviews with this book)

Not a physics major (Pure Math), but did take a course in undergrad that used Taylor's book. Found it clear, and very enjoyable.

Wanting to review my undergrad physics, I purchased a copy of Simon (Symon)? It appears to be at a higher level than Taylor, but readable from first glance. Have not worked through it, but I am sure working through KK is enough preparation, and you may find Taylor boring. Since my intro physics was based on Serway, which is a way easier book than KK.

 

[vanhees71]

1. is the "golden standard" showing that a "gold-standard book" can be ruined by attempts to "modernize it". I don't understand, why textbook writers distort a brillant textbook from the past by rewriting it in a way such that they introduce misconceptions which make the content of the book even contradictory. While they get the non-holonomic dynamics correct using D'Alembert's principle they get it wrong when using the action principle by misunderstanding the meaning of "virtual displacements" and "variations", respectively, (which are analogous, and lead to the same equations of motion, when applied correctly). Thus 2. is clearly better than 1.

I'm not familiar enough with the other books you mention to have an opinion on them.

My favorites are

A. Sommerfeld, Lectures on classical physics, vol. 1 (Sommerfeld's lectures are always my favorite in any classical-physics topic; the only sin is using the $\mathrm{i} c t$ convention in relativity, but since the physics content is so brillantly presented, I'm willing to forgive this major sin ;-)).

Landau and Lifschitz, Course of theoretical physics 1 (the no-nonsense modern approach, starting right away with the action principle and gets also the non-holomic motion right)

Arnold, Mathematical Methods of Classical Mechanics (the mathematicians' modern point of view at Newtonian mechanics)