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Math Help - Inclination of axis

  1. #1
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    Inclination of axis

    have 3 mutually perpendicular axis X' , Y' and Z'

    Line AB lies on X' and I know the global coordinates of A and B [that is coordinates cooresonding to axis X, Y and Z

    I want to find:

    1. Inclination of X' with global X , Y and Z axis.

    2. Inclination of Y' with global X , Y and Z axis.

    3. Inclination of Z' with global X , Y and Z axis.

    Please help--very very urgent!!!
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  2. #2
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    Oct 2008
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    We found a reference wherein the author follows the approach below to determine the directional cosines :

    l1 , m1, n1 -----which are the cosines of the angles between x' axis and the global x, y and z axis

    l2 , m2, n2 -----which are the cosines of the angles between y' axis and the global x, y and z axis

    l3 , m3, n3 -----which are the cosines of the angles between z' axis and the global x, y and z axis

    However, we have not understtod the appraoch.I will describe below what he has done.

    l1 , m1 and n1 is clear; that is;

    l1 = x2 - x1 / length (AB)

    m1 = y2 - y1 / length (AB)

    n1 = z2 - z1 / length (AB)


    Let

    Vx' be a matrix such that

    [Vx' ] = [l1 m1 n1]^T

    Then, he takes a reference point C such that C does not lie along the line joining AB

    Let the coordinates of C be (x3,y3,z3)

    He then gets:

    "V13" where V13 is a matrix

    V13 = [ (x3 - x1) / l13 (y3 - x1) / l13 (z3 - x1) / l13]

    where,

    l13 is the distance between A and the reference point.

    Now,

    [l3 m3 n3] ^T = (Vx ' x V13) / modulus of (Vx ' x V13)

    Let:

    [l3 m3 n3] ^T = Vz'


    Note: (Vx ' x V13) denotes cross product

    Next:

    [l2 m2 n2] ^T = Vz' x Vx'

    Note: (Vz ' x Vx') denotes cross product

    We do not follow the approach above?

    He has not given any explanation for above.

    Whatever, he has given we have described above???
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