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July 30th, 2013, 07:18 AM  #1 
Newbie Joined: Jul 2013 Posts: 4 Thanks: 0  Rotation of a Cartesian Coordinate System
How can I rotate the Cartesian coordinate system ( i=(1,0,0); j=(0,1,0); k=(0,0,1) ) so that angles between new and the old axes be equal to a, b and c, respectively? Here a is angle between i and i' etc. Is there any connection to the Euler angles transformation?

July 30th, 2013, 02:23 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,045 Thanks: 1618 
Do you realize that the angles can't be chosen arbitrarily?

July 30th, 2013, 03:21 PM  #3  
Newbie Joined: Jul 2013 Posts: 4 Thanks: 0  Re: Quote:
 
July 30th, 2013, 04:23 PM  #4 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Rotation of a Cartesian Coordinate System
What angles, exactly, are you talking about? Given a single point, in a three dimensional Cartesian coordinate system, we can define the three angles between the straight line from the origin, (0, 0, 0), to the point and the three (positive) coordinate axes. If we call those angle a, b, and c. However, it can be shown that the three "direction cosines", cos(a), cos(b), cos(c), together, give the unit vector in the direction of that point. That is, we must have .

July 30th, 2013, 04:42 PM  #5  
Newbie Joined: Jul 2013 Posts: 4 Thanks: 0  Re: Rotation of a Cartesian Coordinate System Quote:
So, ? is angle between i and i', ? is angle between j and j' and ? is angle between k and k'.  

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