🚀 go-pugleaf

"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.

Thank you again, and kind regards,

Sergey