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Transformation of a Vector 
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#1
Feb213, 08:31 AM

P: 121

Greetings,
My question is from the book "Tensor Analysis" by Barry Spain. I am asked to show that how a vector transforms from rectangular Cartesian coordinates to polar coordinates. I have attached the question in jpeg format. I have came up with a solution but the angular component in my solution is r^2 times the angular component given in the book. I have checked some books about this subject and found out that both the solution given in the attachment and I have found exist. I am pretty confused about this and I assume that this book is wrong. I will be grateful if someone can provide some insight. 


#2
Feb313, 08:59 AM

P: 121

Any ideas ?



#3
Feb313, 03:09 PM

Sci Advisor
P: 6,040

My guess: normalization question. Both answers may be right.



#4
Feb413, 05:18 PM

P: 22

Transformation of a Vector
Here is a solution based on using vector u_r = [cos(A) , sin(A)] and vector u_A = [sin(A), cos(A)] normal to it. Edit: It appears the answer is not exactly the same.



#5
May813, 04:03 AM

P: 121

P.S The link is not accessible. 


#6
Jun1213, 06:56 PM

P: 121

The link was accessible and I saw the solution which is similar to mine though less detail is provided. The two answers differ by a factor of r and I think the solution in the link you suggest is the correct one, since it has the dimensions of acceleration and this is acceleration am I correct?



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