formula for K_a - Githubissues

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formula for K_a #17

Closed lthiet closed 3 years ago

lthiet commented 3 years ago

hi,

i'm a bit confused about the formula for K_a.

why is there a cross product without a right operand? or is it r_a_x? but it is not defined..

many thanks

benjirer commented 3 years ago

Hey, I was wondering the same thing, did you figure it out?

lthiet commented 3 years ago

yes, check out the function getCrossProductMatrix(). iirc, you can express the cross product as a skew matrix multiplication, this is what the subscript x mean I think.

nwicki commented 3 years ago

Indeed. On the wikipedia page (https://en.wikipedia.org/wiki/Skew-symmetric_matrix) the same notation is also used. The cross product between two vectors a and b (a x b) can be expressed by multiplying b with a matrix initialised with the coefficients of a as depicted here:

Then, we have that a x b = a_x * b, where a_x is the skew symmetric matrix of a.

Edit: However, the impulse equation can actually be represented with only using cross products.