Angular momentum of rigid body elements tensor

[ognik]

Homework Statement

I was working through my text on deriving the tensor for Angular momentum of the sums of elements of a rigid body, I follow it all except for one step. Here is a great page which shows the derivation nicely - http://www.kwon3d.com/theory/moi/iten.html
I follow clearly to the Eq. below

Homework Equations

$$H= \sum_{i} m_{i} [ r_{i}\wedge(\omega\wedge r_{i})] $$

The Attempt at a Solution

The link is as far as I could get, could someone please explain how it goes from the above Eq. to the 3 matrices in the next step?

 

[Delta2]

Well its by the definition of the vector cross product in cartesian coordinate system and by definition of matrix multiplication. It puts proper values inside the matrices, so that the matrix multiplication results in the vector cross product in cartesian coordinates. Maybe this section in wikipedia will help you understand it http://en.wikipedia.org/wiki/Cross_product#Conversion_to_matrix_multiplication and http://en.wikipedia.org/wiki/Cross_product#Computing_the_cross_product

 

[ognik]

Thanks, indeed it does - "The vector cross product also can be expressed as the product of a skew-symmetric matrix and a vector" (not in my textbook, naughty, bad textbook :-))
I also did the (laborious) 'normal' triple vector product calculations, and happily ended with the same answer - guess which way I will be evaluating triple vector products from now on :-)