vector 3

[sky_tm]

i) Je-li

<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$F = y^2 i - 3x^2 j yzk' title="3 $ F = y ^ 2 i - 3x ^ 2 j yzk" alt='3$F = y^2 i - 3x^2 j yzk' align=absmiddle>

, Nájdite

<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\nabla XF' title="3 $ \ nabla XF" alt='3$\nabla XF' align=absmiddle>

a

<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\nabla \bullet F' title="3 $ \ nabla \ strela F" alt='3$\nabla \bullet F' align=absmiddle>ii) Ukážte, že

<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$G = 2xy^3 i (1 3x^2 y^2 )j' title="3 $ G = 2xy ^ 3 i (1 3x ^ 2 y ^ 2) j" alt='3$G = 2xy^3 i (1 3x^2 y^2 )j' align=absmiddle>

Je konzervatívny vektorové pole na celé lietadlo.

iii) Nájdite potenciálne funkcie

<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\Phi ' title="3 $ \ Phi" alt='3$\Phi ' align=absmiddle>

tak, aby

<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\nabla \Phi = G' title="3 $ \ nabla \ Phi = G" alt='3$\nabla \Phi = G' align=absmiddle>

.
Naposledy upravil sky_tm dňa 13 apríla 2006 7:28, upraveno 1 celkom

 

[steve10]

sky_tm Napísal:

i) Je-li
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$F = y^2 i - 3x^2 j yzk' title="3 $ F = y ^ 2 i - 3x ^ 2 j yzk" alt='3$F = y^2 i - 3x^2 j yzk' align=absmiddle> , Nájdite
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\nabla XF' title="3 $ \ nabla XF" alt='3$\nabla XF' align=absmiddle> a
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\nabla XF' title="3 $ \ nabla XF" alt='3$\nabla XF' align=absmiddle>

ii) Ukážte, že
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$G = 2xy^3 i (1 3x^2 y^2 )j' title="3 $ G = 2xy ^ 3 i (1 3x ^ 2 y ^ 2) j" alt='3$G = 2xy^3 i (1 3x^2 y^2 )j' align=absmiddle> Je konzervatívny vektorové pole na celé lietadlo.iii) Nájdite potenciálne funkcie
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\Phi ' title="3 $ \ Phi" alt='3$\Phi ' align=absmiddle> tak, aby
<img src='http://www.elektroda.pl/cgi-bin/mimetex/mimetex.cgi?3$\nabla \Phi = G' title="3 $ \ nabla \ Phi = G" alt='3$\nabla \Phi = G' align=absmiddle> .