Transformation of a Vector


by Septim
Tags: transformation, vector
Septim
Septim is offline
#1
Feb2-13, 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.
Attached Thumbnails
ss.JPG  
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
Septim
Septim is offline
#2
Feb3-13, 08:59 AM
P: 121
Any ideas ?
mathman
mathman is offline
#3
Feb3-13, 03:09 PM
Sci Advisor
P: 5,941
My guess: normalization question. Both answers may be right.

Ferramentarius
Ferramentarius is offline
#4
Feb4-13, 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.
Septim
Septim is offline
#5
May8-13, 04:03 AM
P: 121
Quote Quote by Ferramentarius View Post
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.
I just saw your post much later but I did not understand your argument.

P.S The link is not accessible.
Septim
Septim is offline
#6
Jun12-13, 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?


Register to reply

Related Discussions
dual vector transformation Calculus & Beyond Homework 1
Vector coordinate transformation: Help? Advanced Physics Homework 4
Active transformation of a vector Advanced Physics Homework 0
vector transformation Linear & Abstract Algebra 3
Vector Transformation Linear & Abstract Algebra 1