Dividing Lamé coefficients

  • #1
LagrangeEuler
701
19
Sometimes in calculations authors uses
[tex]\frac{1}{h_1h_2}=\frac{h_3}{h_1h_2h_3}[/tex]
where ##h_i, i=1,2,3## are Lame coefficients. For instance in spherical coordinates ##h_r=1##, ##h_{\theta}=r##, ##h_{\varphi}=r\sin \theta##. I am not sure how we can divide so easily Lame coefficients when some on them obviously can be zero for certain values of parameters. Can someone give me some explanation? Thanks a lot in advance.
 

Answers and Replies

  • #2
anuttarasammyak
Gold Member
1,719
838
I have no background of the physics there but the formula seems multiplying the same number to denominator and numerator, so obviously right except the number is zero.
 
  • #3
36,334
8,293
Changed problem level from A to B. The underlying concept of Lame coefficients might be advanced, but in the posted problem all that was done was to multiply a fraction by 1 in the form of ##h_3## over itself.
 
  • #4
pasmith
Homework Helper
2,334
937
I am not sure how we can divide so easily Lame coefficients when some on them obviously can be zero for certain values of parameters. Can someone give me some explanation? Thanks a lot in advance.

You can divide a function by another function provided that the denominator is not identically zero; this reduces the domain by excluding points where the denominator is zero. In the context of Lame coefficients these are points where the coordinate system breaks down, with a single point being referred to by multiple distinct coordinate tuples. If you need to analyze something at these points, the answer is to use a different coordinate system.
 

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