How to show that the bipolar co-ordinates are othogonal
How to show that the bipolar co-ordinates are othogonal
where $x=dfrac{sin hv}{cos hv-cos u},y=dfrac{sin u}{cos hv-cos u},z=z$
where $uin [0,2pi]$ and $y,zin (-infty,infty)$.
How to show a system is orthogonal?
Do I need to compute the angle between them?If yes how to do it?
linear-algebra analytic-geometry coordinate-systems orthogonality spherical-coordinates
asked Nov 23 at 14:32
Join_PhD
1968
add a comment |
How to show that the bipolar co-ordinates are othogonal
where $x=dfrac{sin hv}{cos hv-cos u},y=dfrac{sin u}{cos hv-cos u},z=z$
where $uin [0,2pi]$ and $y,zin (-infty,infty)$.
How to show a system is orthogonal?
Do I need to compute the angle between them?If yes how to do it?
linear-algebra analytic-geometry coordinate-systems orthogonality spherical-coordinates
asked Nov 23 at 14:32
Join_PhD
1968
add a comment |
How to show that the bipolar co-ordinates are othogonal
where $x=dfrac{sin hv}{cos hv-cos u},y=dfrac{sin u}{cos hv-cos u},z=z$
where $uin [0,2pi]$ and $y,zin (-infty,infty)$.
How to show a system is orthogonal?
Do I need to compute the angle between them?If yes how to do it?
linear-algebra analytic-geometry coordinate-systems orthogonality spherical-coordinates
asked Nov 23 at 14:32
Join_PhD
1968
How to show that the bipolar co-ordinates are othogonal
where $x=dfrac{sin hv}{cos hv-cos u},y=dfrac{sin u}{cos hv-cos u},z=z$
where $uin [0,2pi]$ and $y,zin (-infty,infty)$.
How to show a system is orthogonal?
Do I need to compute the angle between them?If yes how to do it?
linear-algebra analytic-geometry coordinate-systems orthogonality spherical-coordinates
linear-algebra analytic-geometry coordinate-systems orthogonality spherical-coordinates
asked Nov 23 at 14:32
Join_PhD
1968
asked Nov 23 at 14:32
Join_PhD
1968
asked Nov 23 at 14:32
Join_PhD
1968
asked Nov 23 at 14:32
Join_PhD
1968
asked Nov 23 at 14:32
Join_PhD
1968
1968
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
Hint.
Given $x(u,v), y(u,v)$ find
$t_x = (x_u,x_v), , t_y = (y_u, y_v)$
and then verify that
$t_xcdot t_y = 0$
answered Nov 23 at 15:01
Cesareo
8,0883516
what is $t_x,t_y$,i dont get that
– Join_PhD
Nov 23 at 15:04
$t_x =left( frac{partial x}{partial u},frac{partial x}{partial v}right)$ etc.
– Cesareo
Nov 23 at 15:22
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Hint.
Given $x(u,v), y(u,v)$ find
$t_x = (x_u,x_v), , t_y = (y_u, y_v)$
and then verify that
$t_xcdot t_y = 0$
answered Nov 23 at 15:01
Cesareo
8,0883516
what is $t_x,t_y$,i dont get that
– Join_PhD
Nov 23 at 15:04
$t_x =left( frac{partial x}{partial u},frac{partial x}{partial v}right)$ etc.
– Cesareo
Nov 23 at 15:22
add a comment |
Hint.
Given $x(u,v), y(u,v)$ find
$t_x = (x_u,x_v), , t_y = (y_u, y_v)$
and then verify that
$t_xcdot t_y = 0$
answered Nov 23 at 15:01
Cesareo
8,0883516
what is $t_x,t_y$,i dont get that
– Join_PhD
Nov 23 at 15:04
$t_x =left( frac{partial x}{partial u},frac{partial x}{partial v}right)$ etc.
– Cesareo
Nov 23 at 15:22
add a comment |
Hint.
Given $x(u,v), y(u,v)$ find
$t_x = (x_u,x_v), , t_y = (y_u, y_v)$
and then verify that
$t_xcdot t_y = 0$
answered Nov 23 at 15:01
Cesareo
8,0883516
Hint.
Given $x(u,v), y(u,v)$ find
$t_x = (x_u,x_v), , t_y = (y_u, y_v)$
and then verify that
$t_xcdot t_y = 0$
answered Nov 23 at 15:01
Cesareo
8,0883516
answered Nov 23 at 15:01
Cesareo
8,0883516
answered Nov 23 at 15:01
Cesareo
8,0883516
answered Nov 23 at 15:01
Cesareo
8,0883516
8,0883516
what is $t_x,t_y$,i dont get that
– Join_PhD
Nov 23 at 15:04
$t_x =left( frac{partial x}{partial u},frac{partial x}{partial v}right)$ etc.
– Cesareo
Nov 23 at 15:22
add a comment |
what is $t_x,t_y$,i dont get that
– Join_PhD
Nov 23 at 15:04
$t_x =left( frac{partial x}{partial u},frac{partial x}{partial v}right)$ etc.
– Cesareo
Nov 23 at 15:22
what is $t_x,t_y$,i dont get that
– Join_PhD
Nov 23 at 15:04
what is $t_x,t_y$,i dont get that
– Join_PhD
Nov 23 at 15:04
$t_x =left( frac{partial x}{partial u},frac{partial x}{partial v}right)$ etc.
– Cesareo
Nov 23 at 15:22
$t_x =left( frac{partial x}{partial u},frac{partial x}{partial v}right)$ etc.
– Cesareo
Nov 23 at 15:22
add a comment |
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