Thrust configuration matrix for rotatable actuators

A more general representation of (1.6) is,

T = T(a)f = T(a)Ku, where the thrust configuration matrix T(a) g Rnxr varies with the azimuth angles a = [a-t,...,a„ ]T.

The azimuth thruster in the horizontal plane are defined in terms of the column vector t; =

azimuth thruster in the horizontal plane sin a 0

azimuth thruster in the vertical plane where the coordinates (lx , ly , lz ) denotes the location of the actuator with respect the body fixed coordinate system. Similar expressions can be derived for thrusters that are rotatable about the x- and y-axes.

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