Wikipedia

Nabla in verschillende assenstelsels: verschil tussen versies

Interactief door geschiedenis bladeren
← Oudere bewerkingNieuwere bewerking →
Verwijderde inhoud Toegevoegde inhoud
VisueelWikitekst
Madyno (overleg | bijdragen)
34.753 bewerkingen
Geen bewerkingssamenvatting
Madyno (overleg | bijdragen)
34.753 bewerkingen
Geen bewerkingssamenvatting
Regel 1.220:
::<math>
\left(
\frac 1{r^2}\frac{\partial r^2\frac{\partial A_x}{\partial r}}{\partial r}
+
\frac 1{(r\sin(\theta))^2}\frac{\partial^2 A_x}{\partial \phi^2}
+
\frac 1{r^2}\frac{\partial^2 A_x}{\partial \theta^2}
\right)
(A_x)
\cos(\phi)\sin(\theta)
+
Regel 1.232 ⟶ 1.233:
::<math>
\left(
\frac 1{r^2}\frac{\partial r^2\frac{\partial A_y}{\partial r}}{\partial r}
+
\frac 1{(r\sin(\theta))^2}\frac{\partial^2 A_y}{\partial \phi^2}
+
\frac 1{r^2}\frac{\partial^2 A_y}{\partial \theta^2}
\right)
(A_y)
\sin(\phi)\sin(\theta)
+
Regel 1.244 ⟶ 1.246:
::<math>
\left(
\frac 1{r^2}\frac{\partial r^2\frac{\partial A_z}{\partial r}}{\partial r}
+
\frac 1{(r\sin(\theta))^2}\frac{\partial^2 A_z}{\partial \phi^2}
+
\frac 1{r^2}\frac{\partial^2 A_z}{\partial \theta^2}
\right)
(A_z)
\cos(\theta)
=
\,</math>
 
 
::<math>
\left(
\frac 1{r^2}\frac{\partial r^2\frac{\partial A_x}{\partial r}}{\partial r}
+
\frac 1{(r\sin(\theta))^2}\frac{\partial^2 A_x}{\partial \phi^2}
+
\frac 1{r^2}\frac{\partial^2 A_x}{\partial \theta^2}
\right)
(A_r\cos(\phi)\sin(\theta)-A_\phi\sin(\phi)+A_\theta\cos(\phi)\cos(\theta))
\cos(\phi)\sin(\theta)
+
Regel 1.268 ⟶ 1.273:
::<math>
\left(
\frac 1{r^2}\frac{\partial r^2\frac{\partial A_y}{\partial r}}{\partial r}
+
\frac 1{(r\sin(\theta))^2}\frac{\partial^2 A_y}{\partial \phi^2}
+
\frac 1{r^2}\frac{\partial^2 A_y}{\partial \theta^2}
\right)
(A_r\sin(\phi)\sin(\theta)+A_\phi\cos(\phi)+A_\theta\sin(\phi)\cos(\theta))
\sin(\phi)\sin(\theta)
+
Regel 1.280 ⟶ 1.286:
::<math>
\left(
\frac 1{r^2}\frac{\partial r^2\frac{\partial A_z}{\partial r}}{\partial r}
+
\frac 1{(r\sin(\theta))^2}\frac{\partial^2 A_z}{\partial \phi^2}
+
\frac 1{r^2}\frac{\partial^2 A_z}{\partial \theta^2}
\right)
(A_r\cos(\theta)+A_\theta\sin(\theta))
\cos(\theta)
=
\,</math>
 
 
 
::<math>
\frac 1{r^2}\frac{\partial r^2\frac{\partial A_r}{\partial r}}{\partial r}
-
\frac {2}{r^2}A_r
-
\frac 2{r^2\sin(\theta)}\frac{\partial A_\phi}{\partial \phi}
-
\frac {2\cos(\theta)}{r^2\sin(\theta)}A_\theta
+
 
 
 
 
 
\frac 1{r^2}\frac{\partial^2 }{\partial \theta^2}
 
(A_r\cos(\phi)\sin(\theta)-A_\phi\sin(\phi)+A_\theta\cos(\phi)\cos(\theta))
\cos(\phi)\sin(\theta)
+
\,</math>
 
::<math>
\left(
\frac 1{r^2}\frac{\partial r^2\frac{\partial }{\partial r}}{\partial r}
+
\frac 1{(r\sin(\theta))^2}\frac{\partial^2 }{\partial \phi^2}
+
\frac 1{r^2}\frac{\partial^2 }{\partial \theta^2}
\right)
(A_r\sin(\phi)\sin(\theta)+A_\phi\cos(\phi)+A_\theta\sin(\phi)\cos(\theta))
\sin(\phi)\sin(\theta)
+
\,</math>
 
 
::<math>
\left(
\frac 1{r^2}\frac{\partial r^2\frac{\partial }{\partial r}}{\partial r}
+
\frac 1{(r\sin(\theta))^2}\frac{\partial^2 }{\partial \phi^2}
+
\frac 1{r^2}\frac{\partial^2 }{\partial \theta^2}
\right)
(A_r\cos(\theta)+A_\theta\sin(\theta))
\cos(\theta)
=
\,</math>
 
 
 
 
 
 
 
 
 
 
Overgenomen van "https://nl.wikipedia.org/wiki/Nabla_in_verschillende_assenstelsels"