Converting vector in cartesian to cylindrical coordinates
This seems like a trivial question, and I'm just not sure if I'm doing it right.
I have vector in cartesian coordinate system: $vec{N} =yvec{a_x} −2xvec{a_y} + yvec{a_z}$. And I need to represent it in cylindrical coord.
Relevant equations:
$$A_rho=A_xcosphi+A_ysinphi$$
$$A_phi=−A_xsinphi+A_ycosphi$$
$$A_z=A_z$$
What is cofusing me is this: The formula for $phi$ is $phi=arctan(frac{y}{x})$ .
Are those $x$ and $y$ in fact $a_x$ and $a_y$? If so, then for my problem, wouldn't it be $phi=arctan(frac{-2x}{y})$? And do I need to change the unit vectors too?
vectors coordinate-systems
edited Mar 17 '17 at 0:08
Community♦
1
asked Jun 13 '15 at 23:22
user247996user247996
112
add a comment |
This seems like a trivial question, and I'm just not sure if I'm doing it right.
I have vector in cartesian coordinate system: $vec{N} =yvec{a_x} −2xvec{a_y} + yvec{a_z}$. And I need to represent it in cylindrical coord.
Relevant equations:
$$A_rho=A_xcosphi+A_ysinphi$$
$$A_phi=−A_xsinphi+A_ycosphi$$
$$A_z=A_z$$
What is cofusing me is this: The formula for $phi$ is $phi=arctan(frac{y}{x})$ .
Are those $x$ and $y$ in fact $a_x$ and $a_y$? If so, then for my problem, wouldn't it be $phi=arctan(frac{-2x}{y})$? And do I need to change the unit vectors too?
vectors coordinate-systems
edited Mar 17 '17 at 0:08
Community♦
1
asked Jun 13 '15 at 23:22
user247996user247996
112
add a comment |
This seems like a trivial question, and I'm just not sure if I'm doing it right.
I have vector in cartesian coordinate system: $vec{N} =yvec{a_x} −2xvec{a_y} + yvec{a_z}$. And I need to represent it in cylindrical coord.
Relevant equations:
$$A_rho=A_xcosphi+A_ysinphi$$
$$A_phi=−A_xsinphi+A_ycosphi$$
$$A_z=A_z$$
What is cofusing me is this: The formula for $phi$ is $phi=arctan(frac{y}{x})$ .
Are those $x$ and $y$ in fact $a_x$ and $a_y$? If so, then for my problem, wouldn't it be $phi=arctan(frac{-2x}{y})$? And do I need to change the unit vectors too?
vectors coordinate-systems
edited Mar 17 '17 at 0:08
Community♦
1
asked Jun 13 '15 at 23:22
user247996user247996
112
This seems like a trivial question, and I'm just not sure if I'm doing it right.
I have vector in cartesian coordinate system: $vec{N} =yvec{a_x} −2xvec{a_y} + yvec{a_z}$. And I need to represent it in cylindrical coord.
Relevant equations:
$$A_rho=A_xcosphi+A_ysinphi$$
$$A_phi=−A_xsinphi+A_ycosphi$$
$$A_z=A_z$$
What is cofusing me is this: The formula for $phi$ is $phi=arctan(frac{y}{x})$ .
Are those $x$ and $y$ in fact $a_x$ and $a_y$? If so, then for my problem, wouldn't it be $phi=arctan(frac{-2x}{y})$? And do I need to change the unit vectors too?
vectors coordinate-systems
vectors coordinate-systems
edited Mar 17 '17 at 0:08
Community♦
1
asked Jun 13 '15 at 23:22
user247996user247996
112
edited Mar 17 '17 at 0:08
Community♦
1
asked Jun 13 '15 at 23:22
user247996user247996
112
edited Mar 17 '17 at 0:08
Community♦
1
edited Mar 17 '17 at 0:08
Community♦
1
edited Mar 17 '17 at 0:08
Community♦
1
1
asked Jun 13 '15 at 23:22
user247996user247996
112
asked Jun 13 '15 at 23:22
user247996user247996
112
asked Jun 13 '15 at 23:22
user247996user247996
112
112
add a comment |
add a comment |
1 Answer
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A vector field is defined over a region in space $mathbb{R}^3 :$ $(x,y,z)$ or $(r,phi, z)$, whichever coordinate system you may choose to represent this space. Your vector $vec{N}$ should be defined in this space at a position vector $vec{r} = (x,y,z)$ or $(r,phi, z)$. So you need to find
$phi = arctan left( frac{y}{x} right)$
Simply put: A vector field without reference to its position makes no sense in a transformation of coordinates.
answered Sep 21 '18 at 8:37
muralymuraly
1
add a comment |
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1 Answer
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1 Answer
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A vector field is defined over a region in space $mathbb{R}^3 :$ $(x,y,z)$ or $(r,phi, z)$, whichever coordinate system you may choose to represent this space. Your vector $vec{N}$ should be defined in this space at a position vector $vec{r} = (x,y,z)$ or $(r,phi, z)$. So you need to find
$phi = arctan left( frac{y}{x} right)$
Simply put: A vector field without reference to its position makes no sense in a transformation of coordinates.
answered Sep 21 '18 at 8:37
muralymuraly
1
add a comment |
A vector field is defined over a region in space $mathbb{R}^3 :$ $(x,y,z)$ or $(r,phi, z)$, whichever coordinate system you may choose to represent this space. Your vector $vec{N}$ should be defined in this space at a position vector $vec{r} = (x,y,z)$ or $(r,phi, z)$. So you need to find
$phi = arctan left( frac{y}{x} right)$
Simply put: A vector field without reference to its position makes no sense in a transformation of coordinates.
answered Sep 21 '18 at 8:37
muralymuraly
1
add a comment |
A vector field is defined over a region in space $mathbb{R}^3 :$ $(x,y,z)$ or $(r,phi, z)$, whichever coordinate system you may choose to represent this space. Your vector $vec{N}$ should be defined in this space at a position vector $vec{r} = (x,y,z)$ or $(r,phi, z)$. So you need to find
$phi = arctan left( frac{y}{x} right)$
Simply put: A vector field without reference to its position makes no sense in a transformation of coordinates.
answered Sep 21 '18 at 8:37
muralymuraly
1
A vector field is defined over a region in space $mathbb{R}^3 :$ $(x,y,z)$ or $(r,phi, z)$, whichever coordinate system you may choose to represent this space. Your vector $vec{N}$ should be defined in this space at a position vector $vec{r} = (x,y,z)$ or $(r,phi, z)$. So you need to find
$phi = arctan left( frac{y}{x} right)$
Simply put: A vector field without reference to its position makes no sense in a transformation of coordinates.
answered Sep 21 '18 at 8:37
muralymuraly
1
answered Sep 21 '18 at 8:37
muralymuraly
1
answered Sep 21 '18 at 8:37
muralymuraly
1
answered Sep 21 '18 at 8:37
muralymuraly
1
1
add a comment |
add a comment |
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