🚀 go-pugleaf

"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