"Dirk Van de moortel" <dirkvandemoortel@hotmail.Thanks-NoSperm.com> wrote in message news:<c12pae$cd7$1@reader11.wxs.nl>...
> "Sergey Karavashkin" <selftrans@yandex.ru> wrote in message news:a42650fc.0402161443.85012fb@posting.google.com...
> > "Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote in message
>  news:<NHIVb.13987$pC3.12117@news.cpqcorp.net>...
> > > "Sergey Karavashkin" <selftrans@yandex.ru> wrote in message news:a42650fc.0402081450.153f158a@posting.google.com...
> > > > thoovler@excite.com (Igor) wrote in message news:<d434b6c6.0402020056.7de6d18b@posting.google.com>...
> > > > > selftrans@yandex.ru (Sergey Karavashkin) wrote in message news:<a42650fc.0402011435.6e84feaa@posting.google.com>...
> > > > > > Dear Colleagues,
> > > > > >
> > > > > > We open the new volume
> > > >
> > > > [snip]
> > > > > >
> > > > > > Please enjoy reading full text:
> > > > > >
> > > > > > http://angelfire.lycos.com/la3/selftrans/v4_1/contents4.html#grad
> > > > > >
> > > > > > I hope, it will be interesting for many of you, and look forward to
> > > > > > hear your opinion.
> > > > > >
> > > > > > Sergey.
> > > > >
> > > > > There seems to be a mistake on the first page, where you have a scalar
> > > > > function dependent on both the radial coordinate and angle theta.  But
> > > > > when you take the gradient, you only have a radial component but no
> > > > > angular one.  This is why you're concluding that curl grad is not
> > > > > zero, when, once you do it properly, it must be.  Curl grad must
> > > > > always vanish regardless of the nature of the coordinate system.  It's
> > > > > an elementary theorem of vector calculus.  I hope this has been
> > > > > helpful.  Good luck.
> > > >
> > > >
> > > > Dear Igor,
> > > >
> > > > I understand you. You show the most typical reaction to this cycle of
> > > > our papers: "Something is wrong! Where is the mistake?" Merely
> > > > psychologically, you already do not consider how much logic is the
> > > > proof, how much correct is mathematics, you only filter the material,
> > > > seeking the trick.
> > >
> > > Looking at your
> > >    http://selftrans.narod.ru/v4_1/grad/grad02/grad02.html
> > > we immediately see that your equation (4) is wrong since
> > > phi depends on theta in your equation (3).
> > > In your case where alpha is constant and zero, you should
> > > write:
> > >      grad(phi) = @phi/@r e_r + 1/r @phi/@theta e_theta
> > > Your equation (5) for the curl is okay.
> > > So your equation (6) is wrong.
> > >
> > > Compare with the correct expressions for grad in eq (3)
> > > and curl in eq (72) in spherical coordinates:
> > >    http://164.8.13.169/Enciklopedija/math/math/s/s571.htm
> > > Note that:
> > >     your phi is their F
> > >     your alpha is their theta
> > >     your theta is their phi
> > >
> > > You made a very elementary mistake.
> > >
> > > Dirk Vdm
> >
> > Thank you, Dirk. At last I see that someone analyses our work, not
> > trying to thoughtlessly squeeze it into the procrustean bed of dogmas.
> > Though this inaccuracy which you have found does not effect on the
> > conclusion that curl of gradient does not vanish, none the less, I'm
> > very pleased. I fully agree with you, gradient of scalar potential has
> > to contain not only radial but also tangential component. Our analysis
> > that you can find some further in this paper, in the problem of field
> > of oscillating potential source - formula (14) in the page 7 -
> > corroborates this.
> >
> > To show that the inaccuracy you found will not turn to zero the curl
> > of gradient, I have put the derivation to our web site,
> >
> > http://selftrans.narod.ru/v4_1/grad/dirk/dirk.html
> >
> > because, on one hand, I think this question interesting and
> > long-expected, and on the other hand, because the derivation consists
> > of many long computations which are convenient to be read in the
> > standard appearance.
> 
> Sergey, you made a new mistake here.
> On that page
>         http://selftrans.narod.ru/v4_1/grad/dirk/dirk.html
> you "corrected in red" my equation
>         grad(phi) = @phi/@r e_r + 1/r @phi/@theta e_theta
>    to
>         grad(phi) = @phi/@r e_r + 1/r 1/sin(theta) @phi/@theta e_theta
> but that is wrong, since I explicitly referred to
>         http://164.8.13.169/Enciklopedija/math/math/s/s571.htm
> where in their equations (30) and (72), as I added:
>     |  your phi is their F
>     |  your alpha is their theta
>     |  your theta is their phi       !!!
> 
> Since your theta is their phi, my equation
>         grad(phi) = @phi/@r e_r + 1/r @phi/@theta e_theta
> was okay and you should not have introduced the 1/sin(theta).
> After all, this is how *you* derived *your* equation (5).
> 
> So, do try again, check the equations, make the substitutions
>     |  your phi is their F
>     |  your alpha is their theta
>     |  your theta is their phi       !!!and you'll see that
> and verify that indeed
>         curl(grad(phi)) = 0
> It is a very well known elementary theorem.
> 
> Dirk Vdm

No, Dirk. To understand, who of us is correct, determine the axis of
symmetry of the problem and the angle corresponding to this symmetry.
The term of expression that contains this angle will be with the
coefficient 1/r. Both in the Leo's problem (this is seen in his
figure) and in the literature to which I referred responding him, the
angle theta does not correspond to the angle to which the symmetry of
the system relates. So to this term of expression
relates the coefficient 1/sin(theta). Dirk, this is not my wish. This
is the school program. So please see attentively this course to make
sure in what I'm saying.

You can additionally make sure that curl(grad(phi)) =/= 0 looking at
our new dynamic animation of scalar potential produced by dynamic
dipole,

http://selftrans.narod.ru/agfig4.gif

In dynamic fields everything is not so as you used to think. So please
try to grasp what I'm saying before thinking me wrong.

Kind regards,
Sergey