Finding Cartesian Components Using Cross Product for Magnus Force Calculation

[zoner7]

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?

 

[ehild]

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

ehild

 

[zoner7]

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.

 

[Hurkyl]

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.

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