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3.3.1 Nonlinear 6-DOF Rigid-Body<br />
Equations of Motion<br />
Theorem 3.2 (Coriolis-Centripetal Matrix from System Inertia Matrix)<br />
Let M be a 6×6 system inertia matrix defined as:<br />
M M <br />
M 11 M 12<br />
M 21 M 22<br />
0<br />
where M 21 = M 12T . Then the Coriolis-centripetal matrix can always be parameterized such that<br />
C C <br />
C <br />
0 33 SM 11 1 M 12 2 <br />
SM 11 1 M 12 2 <br />
SM 21 1 M 22 2 <br />
where<br />
1 u, v, w , 2 p, q, r <br />
Proof: Sagatun and Fossen (1991).<br />
15<br />
Lecture Notes TTK 4190 Guidance and Control of Vehicles (T. I. Fossen)
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