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where 1 is the 4x4 identity matrix. Equation (16-1) is particularly useful if the axis of rotation does not change over the time interval A/, and is often used in inertial navigation. This is discussed more fully in Section 17.1, as are the errors resulting from the use of Eq. (16-1) when the axis is not strictly constant.

For the case of general attitude motion, it is convenient to convert Eq. (16-1) to a differential equation. In this case, At is infinitesimal and A<J>=<dA/, where <o is the magnitude of the instantaneous angular velocity of the rigid body. We use the small angle approximations

to obtain where Q is the skew-symmetric matrix

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