[rotation] Request for Comment -- Nomenclature Guidelines

John R Evans jrevans at usgs.gov
Fri Jan 25 22:22:13 CET 2008

Dear Alain, Chuck, et al.,

Thanks so much for the ongoing discussion -- it is very helpful.

I quite agree with Alain that rotation is not a "true" vector -- it simply 
does not sum as translational slowness (not velocity) vectors would, for 
example.  I think Chuck's comment about the curl of displacement might be 
appropriate to include in the terminology note if we can all settle on the 
details.  Chuck, please propose specific, compatible notation for all to 
comment on.

As to whether we should distinguish infinitesimal from finite rotations, I 
really don't think we are ready for the simplifications that can be made 
in the limit of zero rotations.  That is for the theorists and 
instrumentalists to tell us, the latter because there is very good 
evidence of serious cross-axis contamination between translational and 
rotational components with current technology.  (Tilts on the order of 10 
urad in strong motion and far smaller for broadband cause serious 
distortion to horizontal translational sensors -- even precision linear 
slides cannot be machined within orders of magnitude of these limits, so 
what is really "infinitesimal" in our business?)

I share Alain's concern that the "pseudo" typically vanishes in usage.  My 
only concern with "axial" is that it does not carry obvious meaning to 
some of us (though we may be in a position to fix this problem).  So how 
should we handle this -- try to enforce the "pseudo", use "axial", 
implicitly recognize that they are "pseudo", ...?

I agree with Chuck and Alain that the definition of a translation-motion 
coordinate system implies the rotational system.  However I think it needs 
saying because there appears to be some confusion on the point.  I amended 
the key sentence to "In Cartesian coordinates, rotations are implied by 
any definition of a translational-motion frame and always should be 
indicated by those physics-based right-hand-rule rotational 
?pseudovectors?, which are oriented along the same axes used for 
translational motions and with the same signs."  OK?

I'll change the time derivatives to dots, as Chuck suggests -- good point. 
 By "partial-arg" do you mean the partial relative to any spatial 

Good point about terminology time vs spatial derivatives if rotation -- 
needs thought and further comment.  For the nonce, let's keep rotational 
velocity et seq. as meaning time derivatives only, as one would expect.

The point about desiring names for the spatial derivatives of rotational 
displacement seems good and to have no obvious answer excepting the 
obvious mathematical representations.  I wonder whether terms like "twist" 
are intended to convey these derivatives??  If so, we need a consensus on 
what term(s) to use.  I would suggest a single term qualified by the axis 
along which the spatial derivative is taken, such as partial-theta/partial 
x being called "twist along the X axis" or "X twist".  I suspect the 
distinction between dots and primes would be too subtle, though I have 
shifted to dots for the time derivatives.  What do you all think?

Pin order matters primarily to instrument folks but clearly does matter 
when you build cables and label channels.  For all others, I think my 
primary point is that we should stick to up-positive Z right-hand systems 
in papers and talks -- (X,Y,Z) which is often (East,North,Up) -- just to 
limit audience pain.

There seems to be a bimodal range of opinions on Wikipedia.  It clearly is 
a very powerful and helpful resource but by the same token not always to 
be trusted.  I dare say that traditional encyclopedias, relying on one or 
a few selected authors per entry, suffer the same or worse tendencies to 
myopic opinionation.   I find it a useful starting place, and that is all 
I meant for the citation to be (it says "For example, ...").

What do the rest of you (IWGoRS) think about "angular" versus "rotational" 
for describing these motions?  I have no strong feelings about either or 
for that matter using them interchangeably.  I suppose simplicity and 
clarity might argue for staying strictly with "rotational" though both are 
well worn terms.

Chuck is right that the term "drift" means something very different to an 
instrumentalist than to a structural engineer.  I have rewritten that 
definition as follows:  "2.     Drift -- This term must be defined by each 
writer because to a structural engineer it means horizontal offsets 
between adjacent floors within a structure (a particular form of strain) 
while to instrumentalists it may mean changes in offset as a function of 
temperature, for example."

The matter of "inferred" versus "point" rotations is critical.  Inferred 
rotations in the near and mid-field are turning out to be a pretty good 
match to linear theory (as are point rotations in the far field) but this 
agreement in stark contrast to point rotations in the near- and mid-field, 
for which we now have several reliable observations.  Near-field point 
rotations are an order of magnitude larger than values inferred from small 
arrays -- a critical conundrum in search of an explanation.  We need to 
keep the distinction at least as long as the conundrum is still hanging 
out there and likely thereafter as well.

Near- and far-field -- by all means, let us await clear definitions from 
the theorists!  In the meantime, define what you mean (above I think I 
mean "out to a few tens of km").

I am not qualified to respond to your comments about "rotational strain" 
-- I was taught just as you were.  But do our Polish colleagues have any 
thoughts on this from the viewpoint of their new continuum theories?  (If 
no such guidance is forthcoming, I'll just drop that term and claim never 
to have written it!)

By the way, Willie and I concur that all of you who comment in any detail 
should become explicit co-authors with me, to be listed alphabetically and 
followed by "... and the Other Members of the International Working Group 
on Rotational Seismology".  OK?

All the best,


Dr. John R. Evans
jrevans at usgs.gov

U.S. Geological Survey
345 Middlefield Rd, MS-977
Menlo Park  CA  94025

All Federal e-mail, outgoing and incoming,
is permanently archived.

Alain Cochard <alain at geophysik.uni-muenchen.de> 
24-01-2008 21:58
Please respond to
alain at geophysik.uni-muenchen.de

"Charles Adam Langston (clangstn)" <clangstn at memphis.edu>
John R Evans <jrevans at usgs.gov>, "rotation at geophysik.uni-muenchen.de" 
<rotation at geophysik.uni-muenchen.de>, Alain Cochard 
<alain at geophysik.uni-muenchen.de>, Alain Cochard 
<Alain.Cochard at eost.u-strasbg.fr>
Re: [rotation] Request for Comment -- Nomenclature Guidelines

Hello group, hello Charles.

Charles Adam Langston (clangstn) writes:

  > Thus, there are no "pseudovectors" and the signs are perfectly defined
  > by the curl.

I don't understand this statement.  Maybe it's a matter of
terminology, but to me the curl, like any cross product of true
vectors actually, is indeed a pseudovector.  Of course I agree when
you say that "Once the Cartesian coordinates have been defined,
rotation is exactly defined", but the fact remains that the
transformation rules for these kind of vectors (also called axial
vectors) are not the same as those for true or usual vectors.
Sometimes the distinction needs to be made.  For example, if one
changes the sign of the basis vectors, trues vectors u and v are
changed into -u and -v, but the cross product is invariant.

I've heard people arguing they shouldn't be called pseudovectors in
the first place, since the 'pseudo' quickly disappears.  They are not
rank-1 tensors, but antisymmetric rank-2 tensors.

Or maybe I'm totally confused...


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