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PrinceOfDarkness
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I don't know if this is the right section, but this problem is in my electromagnetism course (Griffiths text).
This is problem 1.9 of Griffiths (3rd edition) text: Find the transformation matrix R that describes a rotation by 120 degrees about an axis from the origin through the point (1,1,1). The rotation is clockwise as you look down the axis toward origin.
At first, I didn't understand the question (actually I still think I don't understand it). But then I read a book on vectors and tensors that I used as a reference in my vector analysis course last year. I couldn't come up with a solution even then. So I discussed it with a friend.
We came up with the following solution: (phi=120degrees)
(cos phi sin phi) = (-0.5 0.866)
(-sin phi cos phi) (-0.866 -0.5)
I am sorry I can't present it in LaTeX as I am not experienced, but there are square matrices on boths sides of the equation.
But isn't this ridiculously simple? This just tells of rotation of 120 degrees about a certain axis (say x-axis). It doesn't say anything about a new axis coming from origin to point (1,1,1). What more should I do?
A friend put the two components Ay, Az both equal to 1. Multiplied this column vector with the rotation matrix I wrote above, and came up with the value of Ay(prime) and Az(prime). His values were:
Ay(prime)=0.366
Az(prime)=-1.366
But this gives the value of coordinates, not the rotation matrix itself. The question asks for the rotation matrix!
I simply don't understand what I should do with this question. This is basically a chapter on vector analysis, and I have almost done all other questions except this one. This one has been bothering me for days now. I have no idea if my solution is right. I don't even know why the question specifically mentions an axis through (1,1,1), if it only required me to put rotation angle, phi, equal to 120degree!
Any help will be greatly appreciated.
This is problem 1.9 of Griffiths (3rd edition) text: Find the transformation matrix R that describes a rotation by 120 degrees about an axis from the origin through the point (1,1,1). The rotation is clockwise as you look down the axis toward origin.
At first, I didn't understand the question (actually I still think I don't understand it). But then I read a book on vectors and tensors that I used as a reference in my vector analysis course last year. I couldn't come up with a solution even then. So I discussed it with a friend.
We came up with the following solution: (phi=120degrees)
(cos phi sin phi) = (-0.5 0.866)
(-sin phi cos phi) (-0.866 -0.5)
I am sorry I can't present it in LaTeX as I am not experienced, but there are square matrices on boths sides of the equation.
But isn't this ridiculously simple? This just tells of rotation of 120 degrees about a certain axis (say x-axis). It doesn't say anything about a new axis coming from origin to point (1,1,1). What more should I do?
A friend put the two components Ay, Az both equal to 1. Multiplied this column vector with the rotation matrix I wrote above, and came up with the value of Ay(prime) and Az(prime). His values were:
Ay(prime)=0.366
Az(prime)=-1.366
But this gives the value of coordinates, not the rotation matrix itself. The question asks for the rotation matrix!
I simply don't understand what I should do with this question. This is basically a chapter on vector analysis, and I have almost done all other questions except this one. This one has been bothering me for days now. I have no idea if my solution is right. I don't even know why the question specifically mentions an axis through (1,1,1), if it only required me to put rotation angle, phi, equal to 120degree!
Any help will be greatly appreciated.