🚀 go-pugleaf

"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