- #1
chetzread
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Homework Statement
why x is p(cosθ)(sinφ) ? and y=p(sinθ)(cosφ)?
z=p(cosφ)
As we can see, φ is not the angle between p and z ...
Triple integral in polar coordinate
- Thread starter chetzread
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Homework Help Overview
The discussion revolves around the representation of coordinates in spherical coordinates, specifically the relationships between the variables x, y, z, and their expressions in terms of the spherical coordinates p, θ, and φ. Participants are questioning the definitions and interpretations of these angles and their corresponding coordinates.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants are exploring the definitions of angles in spherical coordinates and their relationship to Cartesian coordinates. There are questions about the interpretation of φ and its relation to the z-axis, as well as discussions about the positioning of p in relation to the x-axis.
Discussion Status
The discussion is ongoing, with participants offering differing perspectives on the definitions and relationships of the variables involved. Some guidance has been provided regarding the use of diagrams and the importance of understanding the foundational concepts of polar coordinates before advancing to spherical coordinates.
Contextual Notes
There is mention of confusion arising from a diagram that may not accurately represent the relationships in spherical coordinates. Additionally, participants note the potential for miscommunication regarding the use of Greek letters in the context of these coordinates.
why x is p(cosθ)(sinφ) ? and y=p(sinθ)(cosφ)?
z=p(cosφ)
As we can see, φ is not the angle between p and z ...
- #2
Mr-R
- 123
- 23
Why would you think that?
Well, as I see it, ##\phi## is the angle between ##z## and ##\rho##.
Well, as I see it, ##\phi## is the angle between ##z## and ##\rho##.
- #3
chetzread
- 798
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really? then where is p?Mr-R said:
P is on the same line as x-axis, am i right?
- #4
Mr-R
- 123
- 23
chetzread said:
Nope it is not on the same axis as x. If that was the case then the equation ##x^2+y^2+z^2=\rho^2## wouldn't make sense.
If you are bothered by the provided diagram then just look up another one from another source
- #5
ehild
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- #6
Irene Kaminkowa
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https://www.physicsforums.com/members/chetzread.597855/
You had better start from 2D - the polar coordinates, trying to understand, why x = ρ cos Θ and y = ρ sin Θ.
You had better start from 2D - the polar coordinates, trying to understand, why x = ρ cos Θ and y = ρ sin Θ.
- #7
vela
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That's a really bad figure. No wonder you're confused. Check out the page ehild linked to.chetzread said:
By the way, ##\rho## is the Greek letter rho. It's not P nor p.
- #8
BvU
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Can I also point out that physicists use ##\theta## for the polar angle and ##\phi## for the azimuthal angle ?
Much more consistent with the cylindrical ##(\rho,\phi,z)## coordinate system
So: stay alert to avoid miscommunication !
Much more consistent with the cylindrical ##(\rho,\phi,z)## coordinate system
So: stay alert to avoid miscommunication !
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