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Components of a cross product

  1. Aug 15, 2010 #1
    The pure math of the problem:

    I have two vectors, both of which are expressed in spherical coordinates. I know the magnitudes as well as the polar and azimuthal angles that express these vectors.

    In addition, I have a third vector. I only know the magnitude of this vector, and I need to find its components in Cartesian coordinates. I know that its direction is described by the cross-product of the first two vectors.

    The underlying physics:

    The two vectors that I know are the velocity and angular velocity vectors of a ball flying through the air. I am trying to find the Cartesian components of the Magnus force, which can be described by (w X v), where v is the velocity vector and w is the angular velocity

    In essence, this is a trigonometry problem; nevertheless, I have no idea how to solve it. can anyone lead me in the right direction?
     
    Last edited: Aug 15, 2010
  2. jcsd
  3. Aug 16, 2010 #2

    ehild

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    I would write both v and w in Cartesian coordinates to do the vector product.

    ehild
     
  4. Aug 16, 2010 #3
    I would do that, but the magnitude of the magnus force is not equal to the cross product of the angular velocity and velocity vectors, it is only in that direction.

    I need to multiply the magnitude (I have it) by a mess of trigonometric functions.
     
  5. Aug 16, 2010 #4

    Hurkyl

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    If you are using the cross product to define a direction, then what does its magnitude have to do with anything? :confused:
     
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