Formelsammlung Koordinatensysteme: Unterschied zwischen den Versionen
Aus GET A
Zeile 83: | Zeile 83: | ||
|style="background-color:#dde6f3"|Ortsvektor | |style="background-color:#dde6f3"|Ortsvektor | ||
|style="background-color:#c9d7ec;text-align:center;"| | |style="background-color:#c9d7ec;text-align:center;"| | ||
+ | <math>\vec{\mathbf{r}}=\vec{\mathbf{e}}_x x+\vec{\mathbf{e}}_y y+\vec{\mathbf{e}}_z z</math> | ||
|style="background-color:#dde6f3;text-align:center;"| | |style="background-color:#dde6f3;text-align:center;"| | ||
+ | <math>\vec{\mathbf{r}}=\vec{\mathbf{e}}_{\rho}\rho+\vec{\mathbf{e}}_z z</math> | ||
|style="background-color:#c9d7ec;text-align:center;"| | |style="background-color:#c9d7ec;text-align:center;"| | ||
+ | <math>\vec{\mathbf{r}}=\vec{\mathbf{e}}_r r</math> | ||
|- | |- | ||
|style="background-color:#dde6f3"|Betrag des Ortsvektors | |style="background-color:#dde6f3"|Betrag des Ortsvektors | ||
|style="background-color:#c9d7ec;text-align:center;"| | |style="background-color:#c9d7ec;text-align:center;"| | ||
+ | <math>r=\sqrt{x^2+y^2+z^2}</math> | ||
|style="background-color:#dde6f3;text-align:center;"| | |style="background-color:#dde6f3;text-align:center;"| | ||
+ | <math>r=\sqrt{\rho^2+z^2}</math> | ||
|style="background-color:#c9d7ec;text-align:center;"| | |style="background-color:#c9d7ec;text-align:center;"| | ||
− | + | <math>r=\sqrt{r^2}</math> | |
|- | |- | ||
|style="background-color:#dde6f3"| [[Wegelemente|vektorielles Wegelement]] | |style="background-color:#dde6f3"| [[Wegelemente|vektorielles Wegelement]] |
Version vom 28. August 2012, 11:06 Uhr
Einheitsvektoren |
|
|
|
|
\quad
|
| |
Zusammenhang mit den kartesischen Koordinaten |
|
| |
Umrechnungen |
|
|
|
Ortsvektor |
|
|
|
Betrag des Ortsvektors |
|
|
|
vektorielles Wegelement | |||
Volumenelement | |||
vektorielles Flächenelement |