Accelerating frame of references & their trasformations

[gulsen]

I have various classical mechanics books but none covers this subject. Even Goldstein doesn't. Can someone suggest a book or online resource on the subject?

 

[pervect]

How about some context?

Accelerating frames in special relativity is covered well in MTW' "Gravitation".

Another keyword is bogoliubov transforms, which may be what you're looking for, but I don't have much detailed info on that. Think I've seen that mostly in the context of quantum mechanics in curved spacetime, think they are mentioned in Wald's "General Relativity".

The SR (special relativity) treatment is simpler if it will do what you want.

 

[Galileo]

Classical mechanics in non-inertial frames is treated in almost any classical mechanics book, e.g. Fowles and Cassidy.

Most important application being of course the description of noninertial effects in a uniformly rotating frame such as (approximately) Earth like centrifugal, Coriolis and transverse forces.

 

[gulsen]

pervect, as Galileo stated, and I implied by saying "classical mechanics", I'm clearly talking about accelerating and rotating reference systems in Newtonian physics, and of course their effects such as Coriolis.

Classical mechanics in non-inertial frames is treated in almost any classical mechanics book, e.g. Fowles and Cassidy.

Thanks, but I couldn't find that book in our library :( Any other suggestions?

 

[jtbell]

Other possibilities:

Mechanics, by Keith Symon (now in its third edition)

Classical Dynamics of Particles and Systems, by Stephen Thornton and Jerry Marion (now in its fifth edition; I think earlier editions are by Marion alone)

Newtonian Mechanics, by A. P. French

I don't know about linearly accelerated reference frames, but surely any intermediate-level classical mechanics book should cover rotating reference frames. I remember learning about centrifugal force, Coriolis force and transverse force from an earlier edition of Fowles and Cassiday (by Fowles alone), during my second undergraduate year, over thirty years ago.

 

[pmb_phy]

I have various classical mechanics books but none covers this subject. Even Goldstein doesn't. Can someone suggest a book or online resource on the subject?

Yes. Mechanics 3rd Ed, L.D. Landau and E.M Lif****z. See Section 39 on page 126 Motion in a non-inertial frame of reference. Good luck. I'll try to find more. I believe I have another book which discusses this. I'll see if I can find it.

Pete

ps - Moderator - The program for stripping out certain words has caused a problem. The name of the person hass the "sh*tz" ("i" = "*") word as part of his name. Can this problem be solved?

 

[arildno]

While the proper transformations of ACCELERATIONS of objects between accelerating frames is given in just about any book, it does not follow from this that it is trivial how the AXES of the accelerating frame is related to the frame at rest.

These are typically given in terms of Euler angles, and the relation between the instantaneous angular velocity vector and the rate of change of the Euler angles is, in general, very ugly.

 

[robphy]

ps - Moderator - The program for stripping out certain words has caused a problem. The name of the person hass the "sh*tz" ("i" = "*") word as part of his name. Can this problem be solved?

Lif****z
Evgeny Lifshitz
Евгений Лифшиц

If you quote this post, you'll see how I did it.

However, with this hack, it probably won't be searchable.

 

[anjor]

Classical Mechanics by Irodov discusses it...