Understanding the Dynamics of Rectangular vs Polar/Spherical Unit Vectors

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Discussion Overview

The discussion revolves around the differences between rectangular unit vectors and polar/spherical unit vectors, particularly focusing on why rectangular unit vectors are constant in time while polar and spherical unit vectors are not. The scope includes conceptual clarification regarding the nature of these unit vectors in different coordinate systems.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants propose that rectangular unit vectors remain constant because they are parallel to each other across the same direction, specifically in the x-direction.
  • Others argue that polar and spherical unit vectors change because they are not parallel at different points on the surface defined by their coordinates, such as spheres.
  • A participant questions the clarity of the original inquiry, suggesting a need for more specificity regarding the concept of change in time.
  • One participant expresses understanding of the explanation provided about the nature of the unit vectors in different coordinate systems.

Areas of Agreement / Disagreement

Participants appear to have differing views on the nature of change in unit vectors across coordinate systems, with no consensus reached on the specifics of the inquiry or the implications of the differences.

Contextual Notes

The discussion lacks specific definitions of "change" in the context of unit vectors and does not resolve the assumptions regarding the behavior of these vectors in dynamic scenarios.

delve
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Why are rectangular unit vectors constant in time whereas those of a polar coordinate or spherical coordinate system aren't?
 
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How is anything changing in time? You need to be waaaay more specific.
 
Could you help me figure out how I can be more specific?
 
delve said:
Why are rectangular unit vectors constant in time whereas those of a polar coordinate or spherical coordinate system aren't?

THe unit vector in the x-direction is orthogonal to the surface x=some constant (i.e, planes).

Thus, all these unit vectors in the x-direction are PARALLELL to each other, and thus, essentially, the same vector.

The radial vector, however, is orthogonal to the surface r=some constant (i.e, spheres)

Along each such surface, non-paralllell radial vectors abound, and thus, the unit radial vactor is NOT the same at different points on the surface.
 
I believe that makes sense, thank you!
 

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