Convert from rectangular to Spherical Coordinates

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Discussion Overview

The discussion revolves around the conversion of rectangular (Cartesian) coordinates to spherical coordinates, focusing on the mathematical expressions and relationships between the two systems. Participants explore the definitions and components of spherical coordinates, including the radial, azimuthal, and polar angles, and how they relate to Cartesian coordinates.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question the correctness of various expressions for the position vector in spherical coordinates, particularly the use of angles as components.
  • Others provide definitions for the spherical coordinates: \( r = \sqrt{(x^2 + y^2 + z^2)} \), \( \theta = \arctan{(\frac{y}{x})} \), and \( \phi = \arccos{(\frac{z}{r})} \).
  • A participant suggests that the Cartesian position vector can be expressed in spherical coordinates as \( \vec r = r \hat r \), while others argue about the roles of \( \hat \theta \) and \( \hat \phi \).
  • There are discussions about the dimensionality of the components and whether they can be added together, with some participants asserting that adding vectors of different dimensions is incorrect.
  • Some participants express uncertainty about how to convert Cartesian coordinates to spherical coordinates and seek clarification on the relationships between the unit vectors.
  • A drawing is referenced to illustrate the relationship between the Cartesian and spherical coordinate systems, emphasizing the importance of visualizing the vectors involved.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct expressions for the position vector in spherical coordinates. There are competing views on how to properly define and relate the components of the vectors, and the discussion remains unresolved regarding the correct formulation.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the relationships between the coordinate systems, as well as the varying definitions and conventions used by participants. The mathematical steps involved in the conversion are not fully resolved.

  • #31
Philosophaie said:
What is different?
Does x,y,z not equal r,theta,phi in post #29?

Several of us have already explained to you several times what is wrong with your thinking. You need to go back and read the posts above carefully.
 
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  • #32
No one explained to me that all the direction that I needed was give to me was in ##\hat r##. Thank you everyone trying to make me come to this conclusion.
 
  • #33
Philosophaie said:
No one explained to me that all the direction that I needed was give to me was in ##\hat r##. Thank you everyone trying to make me come to this conclusion.

Posts 19, 21, and 24 all told you that the position vector \vec r = r * \hat r . I'm glad you finally arrived at the correct conclusion.
 
  • #34
Philosophaie said:
No one explained to me that all the direction that I needed was give to me was in ##\hat r##. Thank you everyone trying to make me come to this conclusion.
No, from the beginning everybody posting in this thread tried to tell you that you could not just assume that and help you figure it out for yourself. Then, finally, it was put explicitly in post #19.
 

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