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It is known how reaction wheel to spacecraft body matrix is represented.

But in case of one and two reaction wheel failure condition, how the transformation to spacecraft body is represented?

Can I replace the column vectors by zeroes?

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Reaction wheels are meant for absorbing or releasing the angular momentum from the rest of the body(=Satellite - Reaction Wheel). They are like angular momentum batteries :-)

4 Reaction wheels are generally mounted in either tetrahedral fashion(More common in GeoSats) or 3 orthogonal and 1 is in diagonal mounting.

In case one wheel fails, practically first you have to let the wheel run down, let the body/Wheels absorb its momentum and then only make that Column vector zero(Actually you have to remove it altogether) so that you can take inverse.

However if two wheel fails you loose the ability to control all three pitch, yaw and roll. However, you can still live with 2 Reaction wheel and 3 torquers.

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