🚀 go-pugleaf

"Sergey Karavashkin" <selftrans@yandex.ru> wrote in message
news:a42650fc.0402241512.7788126e@posting.google.com...
> "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,

For *any* scalar function of position phi, it is universally true, as can be
proved in two lines of vector calculus, that
curl(grad(phi)) = 0

What am I missing?

Franz