Results 1 to 3 of 3

Math Help - Determining a rotation in R^3 given angles of new axes w.r.t. original x-axis

  1. #1
    Newbie
    Joined
    Jul 2011
    Posts
    2

    Determining a rotation in R^3 given angles of new axes w.r.t. original x-axis

    The problem is essentially as follows:

    In \mathbb{R}^3, a rotated coordinate system's axes are at angles \phi_1, \phi_2 and \phi_3 to the x-axis in standard Cartesian coordinates. Find the rotation matrix between the two coordinate systems.

    I've tried to attack this both algebraically, using the 3 given direction cosines and orthonormality properties of the rotation matrix, as well as geometrically, trying to use trigonometric relationships between the two coordinate systems, but just can't seem to make it work. Algebraically it gets really messy really quickly and I can't solve for the unknowns and geometrically I can't work out enough useful relationships.

    Any help would be much appreciated. Cheers!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Jun 2011
    Posts
    56

    Re: Determining a rotation in R^3 given angles of new axes w.r.t. original x-axis

    Defining a rotation with angles to the original x-axis is a bit unusual. Do you have a specific reason for using these kind of angles? Much more common is the use of Euler angles.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2011
    Posts
    2

    Re: Determining a rotation in R^3 given angles of new axes w.r.t. original x-axis

    I know that this is non-standard and that Euler angles, quaternions, etc. are the more usual way of paramaterizing such rotations. Though in theory, as SO(3) is 3-dimensional, any arbitrary parameterization is described by 3 numbers as in the problem.

    It comes from here: http://bit.ly/qBH13I, 6.ii).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Rotation and Transformation of Axes
    Posted in the Geometry Forum
    Replies: 4
    Last Post: March 18th 2010, 01:31 AM
  2. Replies: 2
    Last Post: May 24th 2009, 08:42 AM
  3. rotation of axes
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: May 11th 2009, 07:37 PM
  4. volume by rotation about x axis
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 26th 2008, 05:12 AM
  5. Rotation around an axis
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: October 18th 2005, 09:11 PM

Search Tags


/mathhelpforum @mathhelpforum